In [ER van Dam, WH Haemers, Which graphs are determined by their spectrum? Linear
Algebra Appl. 373 (2003), 241–272] we gave a survey of answers to the question of which …

Let G be a graph with n vertices, and let A (G) and D (G) denote respectively the adjacency
matrix and the degree matrix of G. Define A α (G)= α D (G)+(1− α) A (G) for any real α∈[0, 1] …

Abstract Let Γ=(G, σ) be a signed graph, where G is the underlying simple graph and σ: E
(G)→{+,−} is the sign function on the edges of G. In this paper we consider the spectral …

A∞-graph is a graph consisting of two cycles with just a vertex in common. We first look for
some invariants for cospectral graphs, then we introduce a new method to determine the …

A graph G is said to be determined by its Q-spectrum if with respect to the signless Laplacian
matrix Q, any graph having the same spectrum as G is isomorphic to G. The lollipop graph …

We investigate when a complete graph K n with some edges deleted is determined by its
adjacency spectrum. It is shown to be the case if the deleted edges form a matching, a …

The formula for the spectral moment of graphs which is represented by the number of
subgraphs is called the RNS spectral moment formula of graphs. In this paper, the research …

The permanental polynomials of graphs received attention in mathematics and were
investigated in chemistry at almost the same time. Like the characteristic polynomial of a …

Let $ n $ be any positive integer and let $ F_n $ be the friendship (or Dutch windmill) graph
with $2 n+ 1$ vertices and $3 n $ edges. Here we study graphs with the same adjacency …

Several matrices can be associated to a graph such as the adjacency matrix or the
Laplacian matrix. The spectrum of these matrices gives some informations about the …