The Wiener Index of Circulant Graphs

Abstract EN

Circulant graphs are an important class of interconnection networks in parallel and distributed computing.

In this paper, we discuss the relation of the Wiener index and the Harary index of circulant graphs and the largest eigenvalues of distance matrix and reciprocal distance matrix of circulants.

We obtain the following consequence: W / λ = H / μ ; 2 W / n = λ ; 2 H / n = μ , where W, H denote the Wiener index and the Harary index and λ, μ denote the largest eigenvalues of distance matrix and reciprocal distance matrix of circulant graphs, respectively.

Moreover we also discuss the Wiener index of nonregular graphs with cut edges.