The anti-adjacency matrix of a graph is constructed from the distance by keeping each row and column only largest distances. This can be interpreted as opposite adjacency matrix, which instead in distances equal to 1. (anti-)adjacency eigenvalues are those its matrix. Employing novel technique introduced Haemers (2019) [9], we characterize all connected graphs with exactly one positive eigenval...

We describe three weight systems arising from the intersection graphs of chord diagrams (also known as circle graphs). These derive from the determinant and rank of the adjacency matrix of the graph, viewed over Z 2 , and from the rank of a " marked " adjacency matrix. We show that these weight systems are exactly those given by the Conway, HOMFLYPT and Kauffman polynomials, respectively.

topological indices are the numerical value associated with chemical constitution purporting for correlation ofchemical structure with various physical properties, chemical reactivity or biological activity. graph theory is adelightful playground for the exploration of proof techniques in discrete mathematics and its results haveapplications in many areas of sciences. one of the useful indices ...

We consider weighted graphs, where the edge weights are positive definite matrices. The eigenvalues of a graph are the eigenvalues of its adjacency matrix. We obtain a lower bound and an upper bound on the spectral radius of the adjacency matrix of weighted graphs and characterize graphs for which the bounds are attained. 2011 Elsevier Inc. All rights reserved.

Let Gl be the graph obtained from Kl by adhering the root of isomorphic trees T to every vertex of Kl, and dk−j+1 be the degree of vertices in the level j. In this paper we study the spectrum of the adjacency matrix A(Gl) and the Laplacian matrix L(Gl) for all positive integer l, and give some results about the spectrum of the adjacency matrix A(Gl) and the Laplacian matrix L(Gl). By using thes...

This research proposes a useful framework for efficiently computing the state equations in scheduling problems for a class of discrete event systems. We focus on systems in which the precedence relationships are represented by a sparse adjacency matrix. The state equations are linear ones in max-plus algebra, and give the earliest event occurrence times. Even if we use the most efficient algori...

The energy of a graph is the sum of the singular values of its adjacency matrix. A classic inequality for singular values of a matrix sum, including its equality case, is used to study how the energy of a graph changes when edges are removed. One sharp bound and one bound that is never sharp, for the change in graph energy when the edges of a nonsingular induced subgraph are removed, are establ...

In this article, we explain how to calculate the adjacency matrix and the characteristic polynomial of a derived voltage graph when the voltage group is abelian as presented in [1]. We then present a theorem for calculating the adjacency matrix of a derived voltage graph for any voltage group, abelian or non-abelian.