Some inequalities for the Kirchhoff index of graphs

Abstract

Let G be a simple connected graph of order n, sequence of vertex degreesi we denote the multiplicative first Zagreb index of graph, andthe Kirchhoff index of G. In this paper we determine several lower and upper bounds for K f depending on some of the graph parameters such as number of vertices, maximum degree, minimum degree, and number of spanning trees or multiplicative Zagreb index.

An Optimization Problem for Computing Predictive Potential of General Sum/Product-Connectivity Topological Indices of Physicochemical Properties of Benzenoid Hydrocarbons

“…where α ∈ R \ {0}. A detailed mathematical treatment is reported in [27][28][29][30]. The application perspective of SCI α is reported in Gutman and Tošović [11] and Hayat et al [14].…”

A note on general sum-connectivity index

“…For instance, various bounds for the general Randić index have been found in [10], [18] and [21]. And in [1], [11], [12] and [20], bounds for the general sum-connectivity index are obtained. Motivated by such results, we present some new bounds for the general sum-connectivity index in this paper.…”