Three Kirchhoffian Indices of the Cactus Graphs

Abstract

In this paper we give six explicit formulae to compute the Kirchhoff index, the multiplicative degree-Kirchhoff index and the additive degree-Kirchhoff index of the $k$-cactus chain and the cactus graph which can be obtained from a $k$-cactus chain by expanding each of the cut-vertices to a cut edge.