Using an idea of M. Newman, it is proved that if $G$ is a graph with $n$ vertices and ${d_1,dots,d_n}$ is the set of vertex degrees of $G$, then $gcd(2m,d^2)$ divides the determinant of the adjacency matrix of $G$, where $d=gcd(d_1,dots,d_n)$. Possible ...
Adjacency Matrix of Graph Create a directed graph using an edge list, and then find the equivalent adjacency matrix representation of the graph. The adjacency matrix is returned as a sparse matrix. s = [1 1 1 2 2 3]; t = [2 3 4 5 6 7]; G = digraph(s,t) ...
The algebra used to define the nilpotent adjacency matrix of a graph on n vertices is not itself a Clifford algebra, but it can be constructed within the 2n-particle fermion algebra Cl2n,2n{mathcal{C}}ell_{2n,2n}, indicating potential connections to quantum computing....
Bapat, R.B., Souvik Roy: On the adjacency matrix of a block graph, Linear and Multilinear Algebra, to appearRB Bapat and Souvik Roy. On the adjacency matrix of a block graph. Linear and Multilinear Algebra, 62(3):406-418, 2014.
In mathematics and computer science, an adjacency matrix is a means of representing which vertices (or nodes) of a graph are adjacent to which other vertices. Another matrix representation for a graph is the incidence matrix.Specifically, the adjacency matrix of a finite graph G on n vertices ...
An adjacency matrix is used to depict connecting points within a graph. A "1" at the junction of a row and column indicates vertices are connected while a "0" indicates that they are not. In directed graphs, a "1" is only used if they are connected and in the correct order. ...
On the adjacency matrix of a graph. A threshold graph on n vertices is coded by a binary string of length n1. We obtain a formula for the inertia of (the adjacency matrix of) a threshold grap... RJ Wilson - 《Combinatorics》 被引量: 14发表: 0年 On the inverse of the adjacency mat...
AdjMatrix = (1,5) 1 (2,7) 1 >> whos NameSizeBytesClassAttributes AdjMatrix2x782logicalsparse NodeEnds1x216double NodeStarts1x216double Sign in to comment. Categories MATLABMathematicsGraph and Network Algorithms Find more onGraph and Network AlgorithmsinHelp CenterandFile Exchange ...
G is a simple undigraph, A is an adjacency matrix of G, M is an associative matrix of G, and D is a diagonal matrix of the degree of the i-th element of the vertex on the diagonal. Their relationship is: G是简单无向图,A为G的邻接矩阵,M为G的关联矩阵,D是对角线上第i个元素为...
A well-known result in graph theory states that when A is the adjacency matrix of a finite graph G, the entries of A k represent numbers of k-step walks existing in G. However, the adjacency matrix fails to distinguish between walks and "self-avoiding" walks (i.e., walks without ...