Results on Resistance Distance and Kirchhoff Index of Graphs With Generalized Pockets - Liu, Qun; Li, Jiaqi (Frontiers in Physics, 2022)
F, Hv are considered simple connected graphs on n and m + 1 vertices, and v is a specified vertex of Hv and u1, u2, … uk ∈ F. The graph G = G[F, u1, … , uk, Hv] is called a graph with k pockets, obtained by taking one copy of F and k copies of Hv and then attaching the ith copy of Hv to the vertex ui, i = 1, … , k, at the vertex v of Hv. In this article, the closed-form formulas of the resistance distance and the Kirchhoff index of G = G[F, u1, … , uk, Hv] are obtained in terms of the resistance distance and Kirchhoff index F and Hv.