Integral Cayley graphs, a notable subject within spectral graph theory, are graphs constructed from finite groups with the defining property that all eigenvalues of their associated adjacency matrices ...

We say that a graph is Laplacian integral if all its Laplacian eigenvalues are integers. We try to find as many as possible unicyclic and bicyclic graphs for which the Laplacian eigenvalues are ...

Recall that "[a] graph is called Laplacian integral if the eigenvalues of its Laplacian matrix are all integers." 1 This spectral property is of some interest in quantum information theory; as such, I ...

Department of Mathematics and Statistics, Qinghai Minzu University, Xining, China. Since then, much attention has been paid to this topic, but they mainly focus on undirected graphs and integral trees ...

ABSTRACT: For a simple undirected graph G, let A( G ) be the (0, 1) adjacency matrix of G. The Seidel matrix of G, is defined as S( G )=J−I−2A( G ) , where J is the all-one matrix and I is the ...