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 corresponding edge. Let I(G) be the set of newly added vertices, i:e I(G) = V (R(G)) n V (G). The
generalized R-vertex corona of G and Hi for i = 1; 2; :::; n, denoted by R(G)