Kn graph

Solution: In the above graph, there are 2 different colors for four vertices, and none of the edges of this graph cross each other. So. Chromatic number = 2. Here, the chromatic number is less than 4, so this graph is a plane graph. Example 3: In the following graph, we have to determine the chromatic number.

Feb 13, 2022 · The algorithm is quite intuitive and uses distance measures to find k closest neighbours to a new, unlabelled data point to make a prediction. Because of this, the name refers to finding the k nearest neighbors to make a prediction for unknown data. In classification problems, the KNN algorithm will attempt to infer a new data point’s class ... Definition A complete bipartite graph is a graph whose vertices can be partitioned into two subsets V1 and V2 such that no edge has both endpoints in the same subset, and every possible edge that could connect vertices in different subsets is part of the graph.PowerPoint callouts are shapes that annotate your presentation with additional labels. Each callout points to a specific location on the slide, describing or labeling it. Callouts particularly help you when annotating graphs, which you othe...Solution: In the above graph, there are 2 different colors for four vertices, and none of the edges of this graph cross each other. So. Chromatic number = 2. Here, the chromatic number is less than 4, so this graph is a plane graph. Example 3: In the following graph, we have to determine the chromatic number.We color the edges of Kn (a complete graph on n vertices) with a certain number of colors and we ask whether there is a complete subgraph (a clique) of a certain size such that all its edges have the same color. We shall see that this is always true for a su–ciently large n. Note that the question about frienships corresponds to a coloring of K6 with 2 colors, …Free graphing calculator instantly graphs your math problems.For illustration, an FC8,K5 graph is given in Figure 1. (a). Theorem 2. Let m and n be two positive integers with m ≥ 3 and n ≥ 3. Let Cm be a cycle on m vertices and Kn be a complete graph on n vertices. Then rainbow connection number of FCm,Kn is rc (FCm,Kn ) = m2 + 1. Proof.Line graphs are a powerful tool for visualizing data trends over time. Whether you’re analyzing sales figures, tracking stock prices, or monitoring website traffic, line graphs can help you identify patterns and make informed decisions.

Free graphing calculator instantly graphs your math problems.The Graph U-Net model from the "Graph U-Nets" paper which implements a U-Net like architecture with graph pooling and unpooling operations. SchNet The continuous-filter convolutional neural network SchNet from the "SchNet: A Continuous-filter Convolutional Neural Network for Modeling Quantum Interactions" paper that uses the interactions blocks ... In today’s digital world, presentations have become an integral part of communication. Whether you are a student, a business professional, or a researcher, visual aids play a crucial role in conveying your message effectively. One of the mo...$\begingroup$ Distinguishing between which vertices are used is equivalent to distinguishing between which edges are used for a simple graph. Any two vertices uniquely determine an edge in that case.Aug 3, 2022 · That is kNN with k=1. If you constantly hang out with a group of 5, each one in the group has an impact on your behavior and you will end up becoming the average of 5. That is kNN with k=5. kNN classifier identifies the class of a data point using the majority voting principle. If k is set to 5, the classes of 5 nearest points are examined. Can some one help me Find the diameter and radius of complete graph with n vertices, I know how to do it for complete graph with small number of vertices but can generalize to the one with n vertices. graph-theory; Share. Cite. Follow asked Feb 6, 2020 at 1:46. David David. 37 5 5 bronze badges $\endgroup$ 1 $\begingroup$ Start by writing …The KN-1000B series bar graph indicators are capable of processing various inputs including thermocouple, RTD, and analog inputs. The series also supports alarm, transmission, and RS485 communication outputs. The LED bar graph and digital display allows users to easily identify measured values. Panel Meters Bar Gragh Display Multi …X = rand ( 50e3, 20 ); % by default, knn index creation includes self-edges, so use k+1 neighbors = knnindex ( X, 11 ); % create 10-nearest neighbor graph G10 = knngraph ( neighbors, 10 ); % create 4-nearest neighbor graph without recomputing the knn search G4 = knngraph ( neighbors, 4 ); Since computing the knn index is the most expensive ...

23-Dec-2016 ... Semantic Scholar extracted view of "On the genus of the complete tripartite graph Kn, n, 1" by Valentas Kurauskas.Two bipartite graphs and one non-bipartite graph. ... Compute the characteristic path length for each of each of the following graphs: P2k, P2k+1, C2k, C2k+1, Kn, ...A k-regular simple graph G on nu nodes is strongly k-regular if there exist positive integers k, lambda, and mu such that every vertex has k neighbors (i.e., the graph is a regular graph), every adjacent pair of vertices has lambda common neighbors, and every nonadjacent pair has mu common neighbors (West 2000, pp. 464-465). A graph …{"payload":{"allShortcutsEnabled":false,"fileTree":{"torch_geometric/transforms":{"items":[{"name":"__init__.py","path":"torch_geometric/transforms/__init__.py ... K-nearest neighbor or K-NN algorithm basically creates an imaginary boundary to classify the data. When new data points come in, the algorithm will try to predict that to the nearest of the boundary line. Therefore, larger k value means smother curves of separation resulting in less complex models. Whereas, smaller k value tends to overfit …Kneser graph In graph theory, the Kneser graph K(n, k) (alternatively KGn,k) is the graph whose vertices correspond to the k -element subsets of a set of n elements, and where two vertices are adjacent if and only if the two corresponding sets are disjoint. Kneser graphs are named after Martin Kneser, who first investigated them in 1956. Examples

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The chromatic polynomial of a disconnected graph is the product of the chromatic polynomials of its connected components.The chromatic polynomial of a graph of order has degree , with leading coefficient 1 and constant term 0.Furthermore, the coefficients alternate signs, and the coefficient of the st term is , where is the number of …Sep 24, 2019 · K is generally an odd number if the number of classes is 2. When K=1, then the algorithm is known as the nearest neighbour algorithm. This is the simplest case. Suppose P1 is the point, for which label needs to be predicted. Basic steps in KNN. KNN has three basic steps. 1. Calculate the distance. 2. May 5, 2023 · The value of k is very crucial in the KNN algorithm to define the number of neighbors in the algorithm. The value of k in the k-nearest neighbors (k-NN) algorithm should be chosen based on the input data. If the input data has more outliers or noise, a higher value of k would be better. It is recommended to choose an odd value for k to avoid ... The number of edges is greater than or equal to 0 0 and less than or equal to mn m n. There is only one spanning subgraph with 0 0 and mn m n edges. There is only one spanning subgraph with 1 1 edge also. For 2 2 edges there are two if m + n ≥ 4 m + n ≥ 4 and only one otherwise. Then I proceed until I have used up all the possible number of ...3. The chromatic polynomial for Kn K n is P(Kn; t) =tn–– = t(t − 1) … (t − n + 1) P ( K n; t) = t n _ = t ( t − 1) … ( t − n + 1) (a falling factorial power), then the minimal t t such that P(Kn; t) ≠ 0 P ( K n; t) ≠ 0 is n n. Note that this is a polynomial in t t for all n ≥ 1 n ≥ 1.

Kilonewton (kN) can be converted into kilograms (kg) by first multiplying the value of kN by 1000 and then dividing it by earth’s gravity, which is denoted by “g” and is equal to 9.80665 meter per second.Feb 29, 2020. 2. Image source. K-nearest neighbors (kNN) is a supervised machine learning algorithm that can be used to solve both classification and regression tasks. I see kNN …They also determine all graceful graphs Kn − G where G is K1,a with a ≤ n − 2 and where G is a matching Ma with 2a ≤ n. They give graceful labelings for K1, ...the complete graph complete graph, K n K n on nvertices as the (unlabeled) graph isomorphic to [n]; [n] 2 . We also call complete graphs cliques. for n 3, the cycle C n on nvertices as the (unlabeled) graph isomorphic to cycle, C n [n]; fi;i+ 1g: i= 1;:::;n 1 [ n;1 . The length of a cycle is its number of edges. We write C n= 12:::n1. The cycle of length 3 is …Figure 1: Photo via educba.com Introduction. K-Nearest Neighbors is the supervised machine learning algorithm used for classification and regression. It manipulates the training data and classifies the new test data based on distance metrics.De nition: A complete graph is a graph with N vertices and an edge between every two vertices. There are no loops. Every two vertices share exactly one edge. We use the symbol KN for a complete graph with N vertices. How many edges does KN have? How many edges does KN have? KN has N vertices. How many edges does KN have?Given a dataset , the k-NN graph is a directed graph structure, in which each node is directed to its top-knearest neighbors in under a given distance metric. It is a key data structure in manifold learn-ing [3, 19, 20], machine learning [4] and information retrieval [7], etc. The time complexity of building a k-NN graph is ( · 2)when Click and drag your mouse from the top-left corner of the data group (e.g., cell A1) to the bottom-right corner, making sure to select the headers and labels as well. 8. Click the Insert tab. It's near the top of the Excel window. Doing so will open a toolbar below the Insert tab. 9. Select a graph type.K-Nearest Neighbor (KNN) Algorithm Read Discuss Courses Video In this article, we will learn about a supervised learning algorithm that is popularly known as the …

Null Graph. A graph having no edges is called a Null Graph. Example. In the above graph, …

In today’s data-driven world, businesses are constantly gathering and analyzing vast amounts of information to gain valuable insights. However, raw data alone is often difficult to comprehend and extract meaningful conclusions from. This is...In the complete graph Kn (k<=13), there are k* (k-1)/2 edges. Each edge can be directed in 2 ways, hence 2^ [ (k* (k-1))/2] different cases. X !-> Y means "there is no path from X to Y", and P [ ] is the probability. So the bruteforce algorithm is to examine every one of the 2^ [ (k* (k-1))/2] different graphes, and since they are complete, in ...Complete graphs (Kn), where each vertex is connected to all of the other vertices in the graph, are not planar if n ≥ 5. So, K5, K6, K7, …, Kn graphs are not planar. Complete bipartite graphs (Km,n) are not planar if m ≥ 3 and n ≥ 3. We can quickly verify that the K3,3 graph is not planar then.K n is bipartite only when n 2. C n is bipartite precisely when n is even. 5. Describe and count the edges of K n;C n;K m;n. Subtract the number of edges each of these graphs have from n 2 to get the number of edges in the complements. Pictures 1. Draw a directed graph on the 7 vertices f0;1;:::;6gwhere (u;v) is an edge if and only if v 3u (mod 7).De nition: A complete graph is a graph with N vertices and an edge between every two vertices. There are no loops. Every two vertices share exactly one edge. We use the symbol KN for a complete graph with N vertices. How many edges does KN have? How many edges does KN have? KN has N vertices. How many edges does KN have?The chromatic number of Kn is. n; n–1 [n/2] [n/2] Consider this example with K 4. In the complete graph, each vertex is adjacent to remaining (n – 1) vertices. Hence, each vertex requires a new color. Hence the chromatic number of K n = n. Applications of Graph Coloring. Graph coloring is one of the most important concepts in graph theory.STEP 4: Calculate co-factor for any element. STEP 5: The cofactor that you get is the total number of spanning tree for that graph. Consider the following graph: Adjacency Matrix for the above graph will be as follows: After applying STEP 2 and STEP 3, adjacency matrix will look like. The co-factor for (1, 1) is 8.Complete Graph: A complete graph is a graph with N vertices in which every pair of vertices is joined by exactly one edge. The symbol used to denote a complete graph is KN. The symbol used to denote a complete graph is KN. However, the same subgraph will also be selected by interchanging A and A 1. Therefore, the total number of k a,a subgroup is 21(3,3,n−6n) Therefore, subgraphs of k n are isomorphic to k 3,3 = 21(3,3,n−6n). 2.) Let k -s be a graph obtained from Ks due to neglecting one edge. k -s graph is nothing but it can be made. o,n,k n-1 graph can be ...

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Type of returned matrix: ‘connectivity’ will return the connectivity matrix with ones and zeros, and ‘distance’ will return the distances between neighbors according to the given metric. metricstr, default=’minkowski’. Metric to use for distance computation. Default is “minkowski”, which results in the standard Euclidean ... Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack ExchangeDense Graphs: A graph with many edges compared to the number of vertices. Example: A social network graph where each vertex represents a person and each edge represents a friendship. Types of Graphs: 1. Finite Graphs. A graph is said to be finite if it has a finite number of vertices and a finite number of edges. A finite graph is a graph …Solution: In the above graph, there are 2 different colors for four vertices, and none of the edges of this graph cross each other. So. Chromatic number = 2. Here, the chromatic number is less than 4, so this graph is a plane graph. Example 3: In the following graph, we have to determine the chromatic number.The K n-complement of a graph G, denoted by K n − G, is defined as the graph obtained fr om the complete graph K n by removing a set of edges that span G ; if G has n vertices, then K n − G ...Proof about maximum amount of Spanning Trees in Complete Graph Hot Network Questions Top 3% in Reference Letter when applying to YaleA finite graph is planar if and only if it does not contain a subgraph that is a subdivision of K5 or K3,3. A “subgraph” is just a subset of vertices and edges. Subgraphs can be obtained by ...To convert kN/m2 to kg/m2, multiply by approximately 102 seconds squared per meter, which is 1000/9.8 seconds squared per meter. Given a starting unit in kN, or kilonewtons, multiply by 1000 to get the corresponding number of newtons.Aug 23, 2020 · Let’s visualize a dataset on a 2D plane. Picture a bunch of data points on a graph, spread out along the graph in small clusters. KNN examines the distribution of the data points and, depending on the arguments given to the model, it separates the data points into groups. These groups are then assigned a label. K-Nearest Neighbor Classifier Best K Value. I created a KNeighborsClassifier for my dataset adjusting the k hyper-parameter (the number of neighbors) in a for loop. The k value was between 1 and 20. The result was the graph below:"K$_n$ is a complete graph if each vertex is connected to every other vertex by one edge. Therefore if n is even, it has n-1 edges (an odd number) connecting it to other edges. Therefore it can't be Eulerian..." which comes from this answer on Yahoo.com. ….

Definition A complete bipartite graph is a graph whose vertices can be partitioned into two subsets V1 and V2 such that no edge has both endpoints in the same subset, and every …3434-10.2-47E AID: 595 . RID: 175| 23/3/2012 (a) A complete graph has a circuit if and only if.. Also a complete graph is connected.. In a complete graph, degree of each vertex is.. Theorem 1: A graph has an Euler circuit if and only if is connected and every vertex of the graph has positive even degree.. By this theorem, the graph has an Euler circuit if and …Complete graphs (Kn), where each vertex is connected to all of the other vertices in the graph, are not planar if n ≥ 5. So, K5, K6, K7, …, Kn graphs are not planar. Complete bipartite graphs (Km,n) are not planar if m ≥ 3 and n ≥ 3. We can quickly verify that the K3,3 graph is not planar then.Aug 3, 2022 · That is kNN with k=1. If you constantly hang out with a group of 5, each one in the group has an impact on your behavior and you will end up becoming the average of 5. That is kNN with k=5. kNN classifier identifies the class of a data point using the majority voting principle. If k is set to 5, the classes of 5 nearest points are examined. The decomposition of Kn into complete bipartite graphs is explored in [3, 15] and into complete m-partite graphs in [6]. This problem has also been addressed for Kn in connection with trees and forests [10, 13]. The decomposition of Km,n into cycles of length 2k is explored in [14]. The d-cube is the graph Qd whose vertex set is the set of all …are indistinguishable. Then we use the informal expression unlabeled graph (or just unlabeled graph graph when it is clear from the context) to mean an isomorphism class of graphs. Important graphs and graph classes De nition. For all natural numbers nwe de ne: the complete graph complete graph, K n K n on nvertices as the (unlabeled) graph ...1. Introduction. The K-Nearest Neighbors algorithm computes a distance value for all node pairs in the graph and creates new relationships between each node and its k nearest neighbors. The distance is calculated based on node properties. The input of this algorithm is a homogeneous graph.Complete graph K n = n C 2 edges. Cycle graph C n = n edges. Wheel graph W n = 2n edges. Bipartite graph K m,n = mn edges. Hypercube graph Q n = 2 n-1 ⨉n edges. srestha answered Jun 14, 2016. by srestha. comment Follow share this. 4 Comments. Show 13 previous comments. by srestha. commented Aug 8, 2017. reply … Kn graph, 2 Answers. This is a very simple instance of orbit-stabilizer: every permutation of the n n vertices induces an embedding of G G in Kn K n, but two permutations result in the same subgraph iff they differ by an automorphism of G G. Thus the number of distinct subgraphs is just n!/|Aut(G)| n! / | Aut ( G) |., Aug 6, 2015 · The authors suggest that also a symmetrical k-NN could be used for graph initialization (when a point A has another point B as a near neighbor but point B doesn’t have point A as a near neighbor, then the edge isn't created). However this approach is typically not used due to its high computational complexity. , Microsoft Excel is a spreadsheet program within the line of the Microsoft Office products. Excel allows you to organize data in a variety of ways to create reports and keep records. The program also gives you the ability to convert data int..., What is the edge connectivity of Kn, the complete graph on n vertices? In other words, what is the minimum number of edges we must delete to disconnect Kn? W..., So when they say the 'maximum distance' between two points, they mean you choose (x, y) ( x, y), find d(x, y) d ( x, y) which is the minimum length of the path between them, and then define the diameter dG =supx,y∈V(G) d(x, y) d G = sup x, y ∈ V ( G) d ( x, y). That will give you 3 3 here and not 5 5. You see, the distance itself is already ..., A graph that cannot be drawn on a plane without a crossover between its edges is called non-planar. Fig.-1 Fig.-2 Fig.-3 Here, Fig.-1is not planar but Fig.-2 and Fig.-3are planer graphs. Theorem: A connected planar graph with n vertices and e edges has e – n +2 regions. Proof: Here it is sufficient to prove the theorem for a simple graph, because …, Q. Kn denotes _______graph. A. regular. B. simple. C. complete. D. null. Answer» C. complete. View all MCQs in: Discrete Mathematics. Discussion. Comment ..., The authors suggest that also a symmetrical k-NN could be used for graph initialization (when a point A has another point B as a near neighbor but point B doesn’t have point A as a near neighbor, then the edge isn't created). However this approach is typically not used due to its high computational complexity., If KN has 362,880 distinct Hamilton Circuits, then… 3. 62,880 = 6!; N = 7. How many vertices are in the KN graph? 7 VERTICES. What is the degree of each vertex are in the KN graph? 7 -1 = 6. How many edges are in the KN graph?7 *6/2 = 21 edges S. ection 6.3: Traveling Salesman Problems . W. EIGHTED GRAPH: Any graph whose edges have n, May 15, 2019 · The desired graph. I do not have much to say about this except that the graph represents a basic explanation of the concept of k-nearest neighbor. It is simply not a representation of the classification. Why fit & predict. Well this is a basic and vital Machine Learning (ML) concept. , kn-graph: The core crate, containing the intermediate representation and the CPU executor. kn-cuda-sys: The Cuda FFI bindings, generated with rust-bindgen. kn-cuda-eval: The Cuda executor and planner. Quick demo // Load on onnx file into a graph let graph = load_graph_from_onnx_path("test.onnx", false)?, a waste of colors). Since each vertex in Kn is adjacent to every other vertex, no two can share a color. So fewer than n colors can’t possibly work. Similar, the chromatic number for Kn,m is 2. We color one side of the graph with one color and the other side with a second color. In general, however, coloring requires exponential time. There ..., Graphs are beneficial because they summarize and display information in a manner that is easy for most people to comprehend. Graphs are used in many academic disciplines, including math, hard sciences and social sciences., Hamilton path: K n for all n 1. Hamilton cycle: K n for all n 3 2.(a)For what values of m and n does the complete bipartite graph K m;n contain an Euler tour? (b)Determine the length of the longest path and the longest cycle in K m;n, for all m;n. Solution: (a)Since for connected graphs the necessary and su cient condition is that the degree of ..., In a complete graph of 30 nodes, what is the smallest number of edges that must be removed to be a planar graph? 5 Maximum number of edges in a planar graph without $3$- or $4$-cycles, De nition: A complete graph is a graph with N vertices and an edge between every two vertices. There are no loops. Every two vertices share exactly one edge. We use the symbol KN for a complete graph with N vertices. How many edges does KN have? How many edges does KN have? KN has N vertices. How many edges does KN have? , frame. From Table II and graph 2, time period is also less for case 2 and 3 in both brace frame and shear wall frame. As base shear increases time period of models decreases and vise versa. Building with short time period tends to suffer higher accelerations but smaller displacement. Therefore, from table III & IV, graph 3 & 4 story, 3. The chromatic polynomial for Kn K n is P(Kn; t) =tn–– = t(t − 1) … (t − n + 1) P ( K n; t) = t n _ = t ( t − 1) … ( t − n + 1) (a falling factorial power), then the minimal t t such that P(Kn; t) ≠ 0 P ( K n; t) ≠ 0 is n n. Note that this is a polynomial in t t for all n ≥ 1 n ≥ 1., Dense Graphs: A graph with many edges compared to the number of vertices. Example: A social network graph where each vertex represents a person and each edge represents a friendship. Types of Graphs: 1. Finite Graphs. A graph is said to be finite if it has a finite number of vertices and a finite number of edges. A finite graph is a graph …, Complete graphs on n vertices are labeled as {eq}K_n {/eq} where n is a positive integer greater than one. It is possible to calculate the total number of vertices, edges, and the degrees of the ..., So when they say the 'maximum distance' between two points, they mean you choose (x, y) ( x, y), find d(x, y) d ( x, y) which is the minimum length of the path between them, and then define the diameter dG =supx,y∈V(G) d(x, y) d G = sup x, y ∈ V ( G) d ( x, y). That will give you 3 3 here and not 5 5. You see, the distance itself is already ..., graph G = Kn − H in the cases where H is (i) a tree on k vertices, k ≤ n, and (ii) a quasi-threshold graph (or QT-graph for short) on p vertices, p ≤ n. A QT-graph is a graph that contains no induced subgraph isomorphic to P 4 or C 4, the path or cycle on four vertices [7, 12, 15, 21]. Our proofs are 1. based on a classic result known as the complement …, In today’s digital world, presentations have become an integral part of communication. Whether you are a student, a business professional, or a researcher, visual aids play a crucial role in conveying your message effectively. One of the mo..., Kilonewton (kN) can be converted into kilograms (kg) by first multiplying the value of kN by 1000 and then dividing it by earth’s gravity, which is denoted by “g” and is equal to 9.80665 meter per second., Graph Theory - Connectivity. Whether it is possible to traverse a graph from one vertex to another is determined by how a graph is connected. Connectivity is a basic concept in Graph Theory. Connectivity defines whether a graph is connected or disconnected. It has subtopics based on edge and vertex, known as edge connectivity and vertex ..., line and adds one vertex to Kn¨odel graphs on 2k −2 vertices. The added vertex is connected to every vertex in the dominating set of the Kn¨odel graph. In [19], the same method is applied to generalized Kn¨odel graphs, in order to construct broadcast graphs on any odd number of vertices. Adhoc constructions sometimes also provide good ..., Jun 1, 2023 · Given a collection of vectors, the approximate K-nearest-neighbor graph (KGraph for short) connects every vector to its approximate K-nearest-neighbors (KNN for short). KGraph plays an important role in high dimensional data visualization, semantic search, manifold learning, and machine learning. The vectors are typically vector representations ... , k. -vertex-connected graph. A graph with connectivity 4. In graph theory, a connected graph G is said to be k-vertex-connected (or k-connected) if it has more than k vertices and remains connected whenever fewer than k vertices are removed. The vertex-connectivity, or just connectivity, of a graph is the largest k for which the graph is k ..., kn-graph: The core crate, containing the intermediate representation and the CPU executor. kn-cuda-sys: The Cuda FFI bindings, generated with rust-bindgen. kn-cuda-eval: The Cuda executor and planner. Quick demo // Load on onnx file into a graph let graph = load_graph_from_onnx_path("test.onnx", false)?, Hamilton path: K n for all n 1. Hamilton cycle: K n for all n 3 2.(a)For what values of m and n does the complete bipartite graph K m;n contain an Euler tour? (b)Determine the length of the longest path and the longest cycle in K m;n, for all m;n. Solution: (a)Since for connected graphs the necessary and su cient condition is that the degree of ..., 3. Proof by induction that the complete graph Kn K n has n(n − 1)/2 n ( n − 1) / 2 edges. I know how to do the induction step I'm just a little confused on what the left side of my equation should be. E = n(n − 1)/2 E = n ( n − 1) / 2 It's been a while since I've done induction. I just need help determining both sides of the equation., Examples. 1. The complete graph Kn has an adjacency matrix equal to A = J ¡ I, where J is the all-1’s matrix and I is the identity. The rank of J is 1, i.e. there is one nonzero eigenvalue equal to n (with an eigenvector 1 = (1;1;:::;1)).All the remaining eigenvalues are 0. Subtracting the identity shifts all eigenvalues by ¡1, because Ax = (J ¡ I)x = Jx ¡ …, of complete graphs K m × K n, for m, n ≥ 3, is computed and the case K 2 × K n left op en. In [1] a recursive construction for an MCB of K 2 × K n is provided. Here, we present an