Computing the Kirchhoff index and the Wiener index of spiro para-hexagonal cylinder chain

Abstract

Kirchhoff index of a graph is given by the sum of inverses of non-zero Laplacian eigenvalues multiplied with the number of vertices of the graph. It has been studied for several linear and cylinder chains of chemically important graphs, so far. In this paper, we consider the spiro para-hexagonal cylinder chain and find its Kirchhoff index, Wiener index and number of spanning trees. We observe that like many other chain graphs, the ratio of Wiener index and Kirchhoff index approaches to 3 for large graphs belong to this class.