A mixed graph D is a that can be obtained from by orienting some of its edges. Let α primitive n th root unity, then the α−Hermitian adjacency matrix defined to Hα = [hrs] where hrs if rs an arc in D, sr 1 digon and 0 otherwise. In this paper we study cospectrality Hermitian graph.

We show that the adjacency matrices of the intersection graphs of chord diagrams satisfy the 2-term relations of Bar-Natan and Garoufalides [2], and hence give rise to weight systems. Among these weight systems are those associated with the Conway and HOMFLYPT polynomials. We extend these ideas to looking at a space of marked chord diagrams modulo an extended set of 2-term relations, define a s...

We consider weighted graphs, where the edge weights are positive definite matrices. The eigenvalues of a graph are the eigenvalues of its adjacency matrix. In this study the upper bounds for the spectral radius of weighted graphs, which edge weights are positive definite matrices, are compared. Mathematics Subject Classification: 05C50

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.

While powers of the adjacency matrix of a finite graph reveal information about walks on the graph, they fail to distinguish closed walks from cycles. Using elements of an appropriate commutative, nilpotentgenerated algebra, a “new” adjacency matrix can be associated with a random graph on n vertices and |E| edges of nonzero probability. Letting Xk denote the number of k-cycles occurring in a r...

In this paper, we consider the randommatrix ensemble given by (db, dw)-regular graphs onM black vertices andN white vertices, where db ∈ [N γ , N2/3−γ ] for any γ > 0. We simultaneously prove that the bulk eigenvalue correlation statistics for both normalized adjacency matrices and their corresponding covariance matrices are stable for short times. Combined with an ergodicity analysis of the Dy...

let $n$ be any positive integer, the friendship graph $f_n$ consists of $n$ edge-disjoint triangles that all of them meeting in one vertex. a graph $g$ is called cospectral with a graph $h$ if their adjacency matrices have the same eigenvalues. recently in href{http://arxiv.org/pdf/1310.6529v1.pdf}{http://arxiv.org/pdf/1310.6529v1.pdf} it is proved that if $g$ is any graph cospectral with $f_n$...

Adinkras are signed graphs used to study supersymmetry in physics. We provide an introduction these objects, and the properties of their adjacency Laplacian matrices. These matrices each have exactly two distinct eigenvalues (of equal multiplicity), making closely related notions strongly regular graphs. also critical groups Adinkras, particular determine odd components. A novel technique indep...

In this paper, all connected graphs with the fourth largest Laplacian eigenvalue less than two are determined, which are used to characterize all connected graphs with exactly three Laplacian eigenvalues no less than two. Moreover, we determine bipartite graphs such that the adjacency matrices of their line graphs have exactly three nonnegative eigenvalues. © 2003 Elsevier Ltd. All rights reser...