Resistance distance and Kirchhoff index in generalized R-vertex and R-edge corona for graphs

TL;DR

This paper derives explicit formulas for resistance distance and Kirchhoff index in generalized R-vertex and R-edge corona graphs, extending previous results to arbitrary graphs G and Hi.

Contribution

It provides new closed-form formulas for resistance distance and Kirchhoff index in generalized corona graphs, broadening the scope of existing theoretical results.

Findings

Closed-form formulas for resistance distance in generalized corona graphs.

Closed-form formulas for Kirchhoff index in generalized corona graphs.

Results generalize previous specific cases to arbitrary graphs.

Abstract

For a graph G, the graph R(G) of a graph G is the graph obtained by adding a new vertex for each edge of G and joining each new vertex to both end vertices of the correspond- ing edge. Let I(G) be the set of newly added vertices. In this paper, we derive closed-form formulas for resistance distance and Kirchhoff index of generalized R-vertex and R-edge corona whenever G and Hi are arbitrary graph. These results generalize the existing results in [9].