We consider the Norton algebra associated with a Q -polynomial primitive idempotent of adjacency matrix for distance-regular graph. obtain formula product that we find attractive.

We prove that counting copies of any graph F in another graph G can be achieved using basic matrix operations on the adjacency matrix of G. Moreover, the resulting algorithm is competitive for medium-sized F : our algorithm recovers the best known complexity for rooted 6-clique counting and improves on the best known for 9-cycle counting. Underpinning our proofs is the new result that, for a ge...

We give a necessary and sufficient condition for a graph to be bipartite in terms of an eigenvector corresponding to the largest eigenvalue of the adjacency matrix of the graph.

let g be a simple connected graph and {v1, v2, …, vk} be the set of pendent (vertices ofdegree one) vertices of g. the reduced distance matrix of g is a square matrix whose (i,j)–entry is the topological distance between vi and vj of g. in this paper, we obtain the spectrumof the reduced distance matrix of thorn graph of g, a graph which obtained by attaching somenew vertices to pendent vertice...

This work aims to discuss the adjacency matrices, Incidence matrix and Degree of some types plane graphs we usually used them, as complete graphs, cycle graph,…,ect. To find dual graph transformation their for theorems prove general cases.

Different from Laplacian or normal matrix, the properties of the adjacency eigenspace received much less attention. Recent work showed that nodes projected into the adjacency eigenspace exhibit an orthogonal line pattern and nodes from the same community locate along the same line. In this paper, we conduct theoretical studies based on graph perturbation to demonstrate why this line orthogonali...

The spectral moments of the edge adjacency matrix recently have been successfully employed in quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR) studies of alkanes, alkyl halides, benzyl alcohols, and cycloalkanes.1-3 In this work we examined spectral moments of the edge adjacency matrix of benzenoid hydrocarbons. We designed combinatoria...

Spectral graph theory has proven to be a useful tool in the analysis of high-dimensional data sets. Recall that, mathematically, a graph is a collection of objects (nodes) and connections between them (edges); a weighted graph additionally assigns numerical values (weights) to the edges. Graphs are represented by their adjacency whose elements are the weights between the nodes. Spectral graph t...

A graph G with convex-QP stability number (or simply a convex-QP graph) is a graph for which the stability number is equal to the optimal value of a convex quadratic program, say P (G). There are polynomial-time procedures to recognize convex-QP graphs, except when the graph G is adverse or contains an adverse subgraph (that is, a non complete graph, without isolated vertices, such that the lea...

Product graph has been shown as a way for matching subgraphs. This paper reports the extension of the product graph methodology for subgraph matching applied to symbol spotting in graphical documents. Here we focus on the two major limitations of the previous version of the algorithm: (1) spurious nodes and edges in the graph representation and (2) inefficient node and edge attributes. To deal ...