Some extremal graphs with respect to inverse degree

Kexiang Xu; Kinkar Ch Das

doi:10.1016/j.dam.2015.09.004

Some extremal graphs with respect to inverse degree

Kexiang Xu, Kinkar Ch Das

Department of Mathematics

Nanjing University of Aeronautics and Astronautics

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

33 Scopus citations

Abstract

The inverse degree of graph G is defined as ID(G)=_σvεV(G)1_dG(v) where _dG(v) is the degree of vertex v in G. In this paper we have determined some upper and lower bounds on the inverse degree ID(G) for a connected graph G in terms of other graph parameters, such as chromatic number, clique number, connectivity, number of cut edges, matching number. Also the corresponding extremal graphs have been completely characterized.

Original language	English
Pages (from-to)	171-183
Number of pages	13
Journal	Discrete Applied Mathematics
Volume	203
DOIs	https://doi.org/10.1016/j.dam.2015.09.004
State	Published - 20 Apr 2016

Keywords

Chromatic number
Connectivity
Cut edge
Inverse degree
Matching number

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10.1016/j.dam.2015.09.004

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abstract = "The inverse degree of graph G is defined as ID(G)=σvεV(G)1dG(v) where dG(v) is the degree of vertex v in G. In this paper we have determined some upper and lower bounds on the inverse degree ID(G) for a connected graph G in terms of other graph parameters, such as chromatic number, clique number, connectivity, number of cut edges, matching number. Also the corresponding extremal graphs have been completely characterized.",

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AU - Das, Kinkar Ch

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AB - The inverse degree of graph G is defined as ID(G)=σvεV(G)1dG(v) where dG(v) is the degree of vertex v in G. In this paper we have determined some upper and lower bounds on the inverse degree ID(G) for a connected graph G in terms of other graph parameters, such as chromatic number, clique number, connectivity, number of cut edges, matching number. Also the corresponding extremal graphs have been completely characterized.

KW - Chromatic number

KW - Connectivity

KW - Cut edge

KW - Inverse degree

KW - Matching number

UR - https://www.scopus.com/pages/publications/84961836695

U2 - 10.1016/j.dam.2015.09.004

DO - 10.1016/j.dam.2015.09.004

M3 - Article

AN - SCOPUS:84961836695

SN - 0166-218X

VL - 203

SP - 171

EP - 183

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

ER -

Some extremal graphs with respect to inverse degree

Abstract

Keywords

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