The resistance distance and Kirchhoff index on quadrilateral graph and pentagonal graph

The quadrilateral graph Q(G) is obtained from G by replacing each edge in G with two parallel paths of length 1 and 3, whereas the pentagonal graph W(G) is obtained from G by replacing each edge in G with two parallel paths of length 1 and 4. In this paper, closed-form formulas of resistance distance and Kirchhoff index for quadrilateral graph and pentagonal graph are obtained whenever G is an arbitrary graph.