Resistance distance and Kirchhoff index for a class of graphs
type: Item
instance of: scholarly article
title: Resistance distance and Kirchhoff index for a class of graphs
zbMATH Open document ID: 1426.05035
DOI: 10.1155/2018/1028614
author: WanJun Yin
author: ZhengFeng Ming
author: Qun Liu
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: Let \(G [F, V_k, H_v]\) be the graph with \(k\) pockets, where \(F\) is a simple graph of order \(n \geq 1\), \(V_k = \{v_1, v_2, \ldots, v_k \}\) is a subset of the vertex set of \(F, H_v\) is a simple graph of order \(m \geq 2\), and \(v\) is a specified vertex of \(H_v\). Also let \(G [F, E_k, H_{u v}]\) be the graph with \(k\) edge pockets, where \(F\) is a simple graph of order \(n \geq 2, E_k = \{e_1, e_2, \ldots e_k \}\) is a subset of the edge set of \(F, H_{u v}\) is a simple graph of order \(m \geq 3\), and \(u v\) is a specified edge of \(H_{u v}\) such that \(H_{u v} - u\) is isomorphic to \(H_{u v} - v\). In this paper, we derive closed-form formulas for resistance distance and Kirchhoff index of \(G [F, V_k, H_v]\) and \(G [F, E_k, H_{u v}]\) in terms of the resistance distance and Kirchhoff index \(F, H_v\) and \(F, H_{u v}\), respectively.
Mathematics Subject Classification ID: 05C12
Mathematics Subject Classification ID: 05C50
zbMATH DE Number: 7018443
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/1028614
OpenAlex ID: W2905682993
cites work: Generalized inverses. Theory and applications.
cites work: The Schur complement and its applications
cites work: Some results of resistance distance and Kirchhoff index of subdivision vertex-edge corona for graphs
cites work: The {1}-inverse of the Laplacian of subdivision-vertex and subdivision-edge coronae with applications
cites work: Resistance distance in wheels and fans
cites work: On a conjecture concerning spanning tree invariants and loop systems
cites work: On the spectra of graphs with edge-pockets
cites work: The spectra and the signless Laplacian spectra of graphs with pockets
cites work: Resistance distance in subdivision-vertex join and subdivision-edge join of graphs
cites work: Resistance distance and Kirchhoff index of \(R\)-vertex join and \(R\)-edge join of two graphs
cites work: On the Laplacian spectra of graphs with pockets
cites work: Minimizing Kirchhoff index among graphs with a given vertex bipartiteness
cites work: Complete characterization of bicyclic graphs with minimal Kirchhoff index
cites work: A note on block representations of the group inverse of Laplacian matrices
cites work: Resistance distance and the normalized Laplacian spectrum
cites work: Some results on resistance distances and resistance matrices
Wikidata QID: Q128695100
description: scientific article; zbMATH DE number 7018443