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 ...

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 ...

The eigenvalue of a graph is the eigenvalue of its adjacency matrix. A graph G is integral if all of its eigenvalues are integers. In this paper some new classes of integral graphs are constructed.

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 ...

Each integral circulant graph ICG(n, D) is characterised by its order n and a set D of positive divisors of n in such a way that it has vertex set ℤ/nℤ and edge set {(a, b) : a, b ∊ ℤ/nℤ, gcd(a — b, n ...

Abstract: The problem of the invariant description of the graph structure is solved by the vertices differentiation method and by forming on its basis integral graph descriptor (ISD). The process of ...