Resistance Distance and Kirchhoff Index of <inline-formula> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula>-Double Join Graphs

Abstract

Let Q(G) be the graph derived from G by inserting a new vertex into every edge of G and by connecting edges of these new vertices that are on adjacent edges of G, and Q-double join of G, G1 and G2 denoted by GQ v{G1, G2}, is the graph derived from Q(G), G1 and G2, by connecting every old-vertex V (G) of Q(G) with every vertex of G1 and every new-vertex I(G) of Q(G) with every vertex of G2. In this paper, we mainly considered the resistance distance and Kirchhoff index of Q-double join graphs GQ v {G1, G2} of an r-regular graph G and any two graphs of G1 and G2.

Keywords

• Double join graphs
• Laplacian matrix
• Kirchhoff index
• group inverse