AUTHOR=Liu Qun , Li Jiaqi 

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

JOURNAL=Frontiers in Physics

VOLUME=10

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=<p><italic>F</italic>, <italic>H</italic><sub><italic>v</italic></sub> are considered simple connected graphs on <italic>n</italic> and <italic>m</italic> + 1 vertices, and <italic>v</italic> is a specified vertex of <italic>H</italic><sub><italic>v</italic></sub> and <italic>u</italic><sub>1</sub>, <italic>u</italic><sub>2</sub>, … <italic>u</italic><sub><italic>k</italic></sub> ∈ <italic>F</italic>. The graph <italic>G</italic> = <italic>G</italic>[<italic>F</italic>, <italic>u</italic><sub>1</sub>, … , <italic>u</italic><sub><italic>k</italic></sub>, <italic>H</italic><sub><italic>v</italic></sub>] is called a graph with <italic>k</italic> pockets, obtained by taking one copy of <italic>F</italic> and <italic>k</italic> copies of <italic>H</italic><sub><italic>v</italic></sub> and then attaching the <italic>i</italic>th copy of <italic>H</italic><sub><italic>v</italic></sub> to the vertex <italic>u</italic><sub><italic>i</italic></sub>, <italic>i</italic> = 1, … , <italic>k</italic>, at the vertex <italic>v</italic> of <italic>H</italic><sub><italic>v</italic></sub>. In this article, the closed-form formulas of the resistance distance and the Kirchhoff index of <italic>G</italic> = <italic>G</italic>[<italic>F</italic>, <italic>u</italic><sub>1</sub>, … , <italic>u</italic><sub><italic>k</italic></sub>, <italic>H</italic><sub><italic>v</italic></sub>] are obtained in terms of the resistance distance and Kirchhoff index <italic>F</italic> and <italic>H</italic><sub><italic>v</italic></sub>.</p>