The adjacency spectrum of a graph Γ , which is denoted by Spec(Γ ), is the multiset of eigenvalues of its adjacency matrix. We say that two graphs Γ and Γ ′ are cospectral if Spec(Γ ) = Spec(Γ ). In this paper for each prime number p, p ≥ 23, we construct a large family of cospectral non-isomorphic Cayley graphs over the dihedral group of order 2p. © 2016 Elsevier B.V. All rights reserved.

The adjacency spectrum Spec(Γ) of a graph Γ is the multiset of eigenvalues of its adjacency matrix. Two graphs with the same spectrum are called cospectral. A graph Γ is “determined by its spectrum” (DS for short) if every graph cospectral to it is in fact isomorphic to it. A group is DS if all of its Cayley graphs are DS. A group G is Cay-DS if every two cospectral Cayley graphs of G are isomo...

An oriented graph G is a simple undirected graph G with an orientation σ, which assigns to each edge a direction so that G becomes a directed graph. G is called the underlying graph of G, and we denote by Sp(G) the adjacency spectrum of G. Skew-adjacency matrix S(G) of G is introduced, and its spectrum SpS(G ) is called the skew-spectrum of G . The relationship between SpS(G ) and Sp(G) is stud...

A concept related to the spectrum of a graph is that of energy. The energy E(G) of a graph G is equal to the sum of the absolute values of the eigenvalues of the adjacency matrix of G . The Laplacian energy of a graph G is equal to the sum of distances of the Laplacian eigenvalues of G and the average degree d(G) of G. In this paper we introduce the concept of Laplacian energy of fuzzy graphs. ...

A graph is said to be determined by the adjacency spectrum (DS for short) if there is no other nonisomorphic graph with the same spectrum. All connected graphs with index at most √ 2 + √ 5 are known. In this paper, we show that with few exceptions all of these graphs are DS. AMS Subject Classification: 05C50.

The spectrum of a graph G is the set of eigenvalues of the 0–1 adjacency matrix of G. The nullity of a graph is the number of zeros in its spectrum. It is shown that the nullity of the line graph of a tree is at most one. c © 2001 Elsevier Science B.V. All rights reserved.

a concept related to the spectrum of a graph is that of energy. the energy e(g) of a graph g is equal to the sum of the absolute values of the eigenvalues of the adjacency matrix of g . the laplacian energy of a graph g is equal to the sum of distances of the laplacian eigenvalues of g and the average degree d(g) of g. in this paper we introduce the concept of laplacian energy of fuzzy graphs. ...

Eigenvalues of a graph are the eigenvalues of its adjacency matrix. The multiset of eigenvalues is called its spectrum. There are many properties which can be explained using the spectrum like energy, connectedness, vertex connectivity, chromatic number, perfect matching etc. Laplacian spectrum is the multiset of eigenvalues of Laplacian matrix. The Laplacian energy of a graph is the sum of the...

We analyze the spectral distribution of the adjacency matrix and the graph Laplacian for a wide variety of random trees. Using soft arguments which seem to be applicable in a wide variety of settings, we show that the empirical spectral distribution for a number of random tree models, converges to a constant (model dependent) distribution. We also analyze the kernel of the spectrum and prove as...