The minimal Kirchhoff index of graphs with a given number of cut vertices

Kexiang Xu; Hongshuang Liu; Yujun Yang; Kinkar Ch Das

doi:10.2298/FIL1613451X

The minimal Kirchhoff index of graphs with a given number of cut vertices

Kexiang Xu, Hongshuang Liu, Yujun Yang, Kinkar Ch Das

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

The resistance distance was introduced by Klein and Randić as a generalization of the classical distance. The Kirchhoff index Kf(G) of a graph G is the sum of resistance distances between all unordered pairs of vertices. In this paper we determine the extremal graphs with minimal Kirchhoff index among all n-vertex graphs with k cut vertices where 1 ≤ k < {Formula Presented}.

Original language	English
Pages (from-to)	3451-3463
Number of pages	13
Journal	Filomat
Volume	30
Issue number	13
DOIs	https://doi.org/10.2298/FIL1613451X
State	Published - 2016

Keywords

Cut vertex
Graph
Kirchhoff index
Resistance distance

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10.2298/FIL1613451X

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title = "The minimal Kirchhoff index of graphs with a given number of cut vertices",

abstract = "The resistance distance was introduced by Klein and Randi{\'c} as a generalization of the classical distance. The Kirchhoff index Kf(G) of a graph G is the sum of resistance distances between all unordered pairs of vertices. In this paper we determine the extremal graphs with minimal Kirchhoff index among all n-vertex graphs with k cut vertices where 1 ≤ k < \{Formula Presented\}.",

keywords = "Cut vertex, Graph, Kirchhoff index, Resistance distance",

author = "Kexiang Xu and Hongshuang Liu and Yujun Yang and Das, \{Kinkar Ch\}",

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T1 - The minimal Kirchhoff index of graphs with a given number of cut vertices

AU - Xu, Kexiang

AU - Liu, Hongshuang

AU - Yang, Yujun

AU - Das, Kinkar Ch

PY - 2016

Y1 - 2016

N2 - The resistance distance was introduced by Klein and Randić as a generalization of the classical distance. The Kirchhoff index Kf(G) of a graph G is the sum of resistance distances between all unordered pairs of vertices. In this paper we determine the extremal graphs with minimal Kirchhoff index among all n-vertex graphs with k cut vertices where 1 ≤ k < {Formula Presented}.

AB - The resistance distance was introduced by Klein and Randić as a generalization of the classical distance. The Kirchhoff index Kf(G) of a graph G is the sum of resistance distances between all unordered pairs of vertices. In this paper we determine the extremal graphs with minimal Kirchhoff index among all n-vertex graphs with k cut vertices where 1 ≤ k < {Formula Presented}.

KW - Cut vertex

KW - Graph

KW - Kirchhoff index

KW - Resistance distance

UR - https://www.scopus.com/pages/publications/85008325094

U2 - 10.2298/FIL1613451X

DO - 10.2298/FIL1613451X

M3 - Article

AN - SCOPUS:85008325094

SN - 0354-5180

VL - 30

SP - 3451

EP - 3463

JO - Filomat

JF - Filomat

IS - 13

ER -

The minimal Kirchhoff index of graphs with a given number of cut vertices

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Keywords

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