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