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.

A mixed graph is said to be second kind hermitian integral (HS-integral) if the eigenvalues of its Hermitian-adjacency matrix are integers. called Eisenstein (0, 1)-adjacency We characterize set S for which normal Cayley Cay(Γ,S) HS-integral any finite group Γ. further show that a and only it integral. This paper generalizes results Kadyan Bhattacharjy (2022) [11].

The energy of a molecular graph G is defined as the summation of the absolute values of the eigenvalues of adjacency matrix of a graph G. In this paper, an infinite class of fullerene graphs with 10n vertices, n ≥ 2, is considered. By proving centrosymmetricity of the adjacency matrix of these fullerene graphs, a lower bound for its energy is given. Our method is general and can be extended to ...

Graph properties suitable for the classification of instance hardness for the NP-hard MAX-CUT problem are investigated. Eigenvalues of the adjacency matrix of a graph are demonstrated to be promising indicators of its hardness as a MAX-CUT instance.

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. ...

The energy of a graph G is equal to the sum of absolute values of the eigenvalues of the adjacency matrix of G, whereas the Laplacian energy of a graph G is equal to the sum of the absolute value of the difference between the eigenvalues of the Laplacian matrix of G and the average degree of the vertices of G. Motivated by the work from Sharafdini an...

There is a connection between the expansion of a graph and the eigengap (or spectral gap) of the normalized adjacency matrix (that is, the gap between the first and second largest eigenvalues). Recall that the largest eigenvalue of the normalized adjacency matrix is 1; denote it by λ1 and denote the second largest eigenvalue by λ2. We will see that a large gap (that is, small λ2) implies good e...

The energy of a graph is the sum of the absolute values of the eigenvalues of its adjacency matrix. Two graphs are equienergetic if they have the same energy. We construct infinite families of graphs equienergetic with edge-deleted subgraphs.

Upper and lower bounds are obtained for the spread 1 n of the eigenvalues 1 2 n of the adjacency matrix of a simple graph. MSC: 05C50, 15A42; 15A36

A graph can be associated with a matrix in several ways. For instance, by associating the vertices of the graph to the rows/columns and then using 1 to indicate an edge and 0 otherwise we get the adjacency matrix A. The combinatorial Laplacian matrix is defined by L = D − A where D is a diagonal matrix with diagonal entries the degrees and A is again the adjacency matrix. Both of these matrices...