Determining graphs by the complementary spectrum

The spectrum of the hyper-star graphs and their line graphs

Let n 1 be an integer. The hypercube Qn is the graph whose vertex set isf0;1gn, where two n-tuples are adjacent if they differ in precisely one coordinate. This graph has many applications in Computer sciences and other area of sciences. Inthe graph Qn, the layer Lk is the set of vertices with exactly k 1’s, namely, vertices ofweight k, 1 k n. The hyper-star graph B(n;k) is...

Self-complementary circulant graphs

Which graphs are determined by their spectrum?

For almost all graphs the answer to the question in the title is still unknown. Here we survey the cases for which the answer is known. Not only the adjacency matrix, but also other types of matrices, such as the Laplacian matrix, are considered. © 2003 Elsevier Inc. All rights reserved.

Reconstruction of Weighted Graphs by their Spectrum

On the structure of self-complementary graphs

A graph G is self complementary if it is isomorphic to its complement G. In this paper we define bipartite self-complementary graphs, and show how they can be used to understand the structure of self-complementary graphs. For G a selfcomplementary graph of odd order, we describe a decomposition of G into edge disjoint subgraphs, one of which is a bipartite self-complementary graph of order |G|−...