AUTHOR=Liu Qun , Li Jiaqi 

TITLE=Results on Resistance Distance and Kirchhoff Index of Graphs With Generalized Pockets

JOURNAL=Frontiers in Physics

VOLUME=Volume 10 - 2022

YEAR=2022

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2022.872798

DOI=10.3389/fphy.2022.872798

ISSN=2296-424X

ABSTRACT=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.