Results on Resistance Distance and Kirchhoff Index of Graphs With Generalized Pockets - Liu, Qun; Li, Jiaqi (Frontiers in Physics, 2022)
Let F,Hv be simple connected graphs on n and m + 1 vertices, respectively. Let v be a specified vertex of Hvand u1,u2,...uk∈ F. Then the graph G = G[F,u1,...,uk,Hv] obtained by taking one copy of F and k copies of Hv, and then attaching the ith copy of Hvto the vertex ui,i = 1,...,k, at the vertex v of Hv(identify uiwith the vertex v of the ith copy) is called a graph with k pockets. In [12], Barik gave the Laplacian spectrum for more general cases. In this paper, we derive closed-form formulas for resistance distance and Kirchhoff index of G = G[F,u1,...,uk,Hv] in terms of the resistance distance and Kirchhoff index F and Hv, respectively.