Let −→ G be a digraph and A( −→ G) be the adjacency matrix of −→ G . Let D( −→ G) be the diagonal matrix with outdegrees of vertices of −→ G and Q( −→ G) = D( −→ G) + A( −→ G) be the signless Laplacian matrix of −→ G . The spectral radius of Q( −→ G) is called the signless Laplacian spectral radius of −→ G . In this paper, we determine the unique digraph which attains the maximum (or minimum) s...

For a k-uniform hypergraph H, we obtain some trace formulas for the Laplacian tensor of H, which imply that ∑n i=1 d s i (s = 1, . . . , k) is determined by the Laplacian spectrum of H, where d1, . . . , dn is the degree sequence of H. Using trace formulas for the Laplacian tensor, we obtain expressions for some coefficients of the Laplacian polynomial of a regular hypergraph. We give some spec...

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 structure of the graph and the question “Which graphs are determined by their spectrum?” remains a difficult problem in algebraic graph theory. In this article we enlarge the known families of graphs determined by their spectrum by ...

The spectrum of a graph has been widely used in graph theory to characterise the properties of a graph and extract information from its structure. It has been less popular as a representation for pattern matching for two reasons. Firstly, more than one graph may share the same spectrum. It is well known, for example, that very few trees can be uniquely specified by their spectrum. Secondly, the...

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: ...

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.

The spectrum of the ∂-Neumann Laplacian on a polydisc in C is explicitly computed. The calculation exhibits that the spectrum consists of eigenvalues, some of which, in particular the smallest ones, are of infinite multiplicity.