Resistance distance in subdivision-vertex join and subdivision-edge join of graphs

The subdivision graph S(G) of a graph G is the graph obtained by inserting a new vertex into every edge of G. Let G1∪G2 be the disjoint union of two graphs G1 and G2. The subdivision-vertex join of G1 and G2, denoted by G1∨˙G2, is the graph obtained from S(G1)∪G2 by joining every vertex in V(G1) to every vertex in V(G2). The subdivision-edge join of G1 and G2, denoted by G1⊻G2, is the graph obtained from S(G1)∪G2 by joining every vertex in I(G1) to every vertex in V(G2), where I(G1) is the set of inserted vertices of S(G1). In this paper, formulae for resistance distance in G1∨˙G2 and G1⊻G2 are obtained.