Development of some novel resistance distance based topological indices for certain special types of graph networks

Abstract

Abstract A graph network consisting of nodes and edges, forms an electrical network if its edges are replaced by a unit resistor. The resistance distance between any two nodes of a connected network is defined as the net effective resistance between them. This work derives mathematical closed form expressions for the resistance distance based topological indices of four families of graph networks such as S n , S n + , S n 2 and S n * . Firstly, we compute the multiplicative eccentricity resistance-distance sum index, multiplicative degree-Kirchhoff index and the reciprocal degree resistance-distance index for the four families of graphs. Secondly, we introduce some new versions of resistance distance based topological indices viz. the additive reciprocal degree-Kirchhoff index, the additive reciprocal eccentric resistance-distance index, the reciprocal eccentric resistance distance index, modified eccentric resistance distance index and the modified degree resistance distance index for the above four families of graph networks. These resistance distance based topological indices are introduced for the first time in the literature, which can surely be useful to investigate the electrical networks.