Let G be a finite group, S ⊆ G \ {1} be a set such that if a ∈ S, then a−1 ∈ S, where 1 denotes the identity element of G. The undirected Cayley graph Cay(G, S) ofG over the set S is the graphwhose vertex set is G and two vertices a and b are adjacent whenever ab−1 ∈ S. The adjacency spectrum of a graph is the multiset of all eigenvalues of the adjacency matrix of the graph. A graph is called i...

The D-eigenvalues {μ1, μ2, . . . , μn} of a graph G are the eigenvalues of its distance matrix D and form the D-spectrum of G denoted by specD(G) . The D-energy ED(G) of the graph G is the sum of the absolute values of its D-eigenvalues. We describe here the distance spectrum of some self-complementary graphs in the terms of their adjacency spectrum. These results are used to show that there ex...

In this paper the properties of node-node adjacency matrix in acyclic digraphs are considered. It is shown that topological ordering and node-node adjacency matrix are closely related. In fact, first the one to one correspondence between upper triangularity of node-node adjacency matrix and existence of directed cycles in digraphs is proved and then with this correspondence other properties of ...

A method based on eigenvalue computations is formulated for computing the Chrestenson spectrum of a discrete p-valued function. This technique is developed by considering an extension to the same approach of computation of the Walsh spectrum for a twovalued function and is then generalized to the p-valued case. Algebraic groups are formulated that correspond to Cayley color graphs based on the ...

Abstract Graphs can be associated with a matrix according to some rule and we find the spectrum of graph respect that matrix. Two graphs are cospectral if they have same spectrum. Constructions help us establish patterns about structural information not preserved by We generalize construction for previously given distance Laplacian larger family graphs. In addition, show appropriate assumptions...

In this first talk we will introduce three of the most commonly used types of matrices in spectral graph theory. They are the adjacency matrix, the combinatorial Laplacian, and the normalized Laplacian. We also will give some simple examples of how the spectrum can be used for each of these types.

Abstract In this paper, we give the spectrum of a matrix by using the quotient matrix, then we apply this result to various matrices associated to a graph and a digraph, including adjacency matrix, (signless) Laplacian matrix, distance matrix, distance (signless) Laplacian matrix, to obtain some known and new results. Moreover, we propose some problems for further research. AMS Classification: ...

Some combinatorial and spectral properties of König-Egerváry (K-E) graphs are presented. In particular, some new combinatorial characterizations of K-E graphs are introduced, the Laplacian spectrum of particular families of K-E graphs is deduced, and a lower and upper bound on the largest and smallest adjacency eigenvalue, respectively, of a K-E graph are determined.

It is proved that the Cartesian product of an odd cycle with the complete graph on 2 vertices, is determined by the spectrum of the adjacency matrix. We also present some computational results on the spectral characterization of cubic graphs on at most 20 vertices. AMS Subject Classification: 05C50.

The spectrum of the Laplacian, signless Laplacian and adjacency matrices of the family of the weighted graphs R{H}, obtained from a connected weighted graph R on r vertices and r copies of a modified Bethe tree H by identifying the root of the i-th copy of H with the i-th vertex of R, is determined.