Generalized Spectral Characterization of Mixed Graphs

Spectral Characterization of Generalized Cocktail-Party Graphs

In the paper, we prove that all generalized cocktail-party graphs with order at least 23 are determined by their adjacency spectra.

Spectral Characterization of Some Generalized Odd Graphs

Suppose G is a connected, k-regular graph such that Spec…G† ˆ Spec…G† where G is a distance-regular graph of diameter d with parameters a1 ˆ a2 ˆ ˆ adÿ1 ˆ 0 and ad > 0; i.e., a generalized odd graph, we show that G must be distance-regular with the same intersection array as that of G in terms of the notion of Ho ̈man Polynomials. Furthermore, G is isomorphic to G if G is one of the odd polygon ...

Generalized Spectral Characterization of Graphs Revisited

A graph G is said to be determined by its generalized spectrum (DGS for short) if for any graph H, H and G are cospectral with cospectral complements implies that H is isomorphic to G. Wang and Xu (2006) gave some methods for determining whether a family of graphs are DGS. In this paper, we shall review some of the old results and present some new ones along this line of research. More precisel...

Spectral characterization of mixed extensions of small graphs

A mixed extension of a graph G is a graph H obtained from G by replacing each vertex of G by a clique or a coclique, where vertices of H coming from different vertices of G are adjacent if and only if the original vertices are adjacent in G. If G has no more than three vertices, H has all but at most three adjacency eigenvalues equal to 0 or −1. In this paper we consider the converse problem, a...

Order unicyclic mixed graphs by spectral radius