The Kirchhoff index of quasi-tree graphs

Kexiang Xu; Hongshuang Liu; Kinkar Ch Das

doi:10.1515/zna-2014-0230

The Kirchhoff index of quasi-tree graphs

Kexiang Xu, Hongshuang Liu, Kinkar Ch Das

Department of Mathematics

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

7 Scopus citations

Abstract

Resistance distance was introduced by Klein and Randić as a generalisation 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 article we characterise the extremal graphs with the maximal Kirchhoff index among all non-trivial quasi-tree graphs of order n. Moreover, we obtain a lower bound on the Kirchhoff index for all non-trivial quasi-tree graphs of order n.

Original language	English
Pages (from-to)	135-139
Number of pages	5
Journal	Zeitschrift fur Naturforschung - Section A Journal of Physical Sciences
Volume	70
Issue number	3
DOIs	https://doi.org/10.1515/zna-2014-0230
State	Published - 2015

Keywords

Distance
Kirchhoff index
Laplacian spectrum
Quasi-rree graph

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abstract = "Resistance distance was introduced by Klein and Randi{\'c} as a generalisation 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 article we characterise the extremal graphs with the maximal Kirchhoff index among all non-trivial quasi-tree graphs of order n. Moreover, we obtain a lower bound on the Kirchhoff index for all non-trivial quasi-tree graphs of order n.",

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AU - Liu, Hongshuang

AU - Das, Kinkar Ch

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AB - Resistance distance was introduced by Klein and Randić as a generalisation 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 article we characterise the extremal graphs with the maximal Kirchhoff index among all non-trivial quasi-tree graphs of order n. Moreover, we obtain a lower bound on the Kirchhoff index for all non-trivial quasi-tree graphs of order n.

KW - Distance

KW - Kirchhoff index

KW - Laplacian spectrum

KW - Quasi-rree graph

UR - https://www.scopus.com/pages/publications/84930239888

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DO - 10.1515/zna-2014-0230

M3 - Article

AN - SCOPUS:84930239888

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JO - Zeitschrift fur Naturforschung - Section A Journal of Physical Sciences

JF - Zeitschrift fur Naturforschung - Section A Journal of Physical Sciences

IS - 3

ER -

The Kirchhoff index of quasi-tree graphs

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