Complete characterization of graphs for direct comparing Zagreb indices

Batmend Horoldagva; Kinkar Ch Das; Tsend Ayush Selenge

doi:10.1016/j.dam.2016.07.008

Complete characterization of graphs for direct comparing Zagreb indices

Batmend Horoldagva, Kinkar Ch Das, Tsend Ayush Selenge

Department of Mathematics

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

38 Scopus citations

Abstract

The classical first and second Zagreb indices of a graph G are defined as M₁(G)=∑_v∈Vd_G(v)² and M₂(G)=∑_uv∈E(G)d_G(u)d_G(v), where d_G(v) is the degree of the vertex v of graph G. Recently, Furtula et al. (2014) studied the difference between the Zagreb indices and mentioned a problem to characterize the graphs for which M₁(G)>M₂(G) or M₁(G)<M₂(G) or M₁(G)=M₂(G). In this paper we completely solve this problem.

Original language	English
Pages (from-to)	146-154
Number of pages	9
Journal	Discrete Applied Mathematics
Volume	215
DOIs	https://doi.org/10.1016/j.dam.2016.07.008
State	Published - 31 Dec 2016

Keywords

First Zagreb index
Graph
Second Zagreb index

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10.1016/j.dam.2016.07.008

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title = "Complete characterization of graphs for direct comparing Zagreb indices",

abstract = "The classical first and second Zagreb indices of a graph G are defined as M1(G)=∑v∈VdG(v)2 and M2(G)=∑uv∈E(G)dG(u)dG(v), where dG(v) is the degree of the vertex v of graph G. Recently, Furtula et al. (2014) studied the difference between the Zagreb indices and mentioned a problem to characterize the graphs for which M1(G)>M2(G) or M1(G)2(G) or M1(G)=M2(G). In this paper we completely solve this problem.",

keywords = "First Zagreb index, Graph, Second Zagreb index",

author = "Batmend Horoldagva and Das, \{Kinkar Ch\} and Selenge, \{Tsend Ayush\}",

note = "Publisher Copyright: {\textcopyright} 2016 Elsevier B.V.",

year = "2016",

month = dec,

day = "31",

doi = "10.1016/j.dam.2016.07.008",

language = "English",

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journal = "Discrete Applied Mathematics",

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T1 - Complete characterization of graphs for direct comparing Zagreb indices

AU - Horoldagva, Batmend

AU - Das, Kinkar Ch

AU - Selenge, Tsend Ayush

PY - 2016/12/31

Y1 - 2016/12/31

N2 - The classical first and second Zagreb indices of a graph G are defined as M1(G)=∑v∈VdG(v)2 and M2(G)=∑uv∈E(G)dG(u)dG(v), where dG(v) is the degree of the vertex v of graph G. Recently, Furtula et al. (2014) studied the difference between the Zagreb indices and mentioned a problem to characterize the graphs for which M1(G)>M2(G) or M1(G)2(G) or M1(G)=M2(G). In this paper we completely solve this problem.

AB - The classical first and second Zagreb indices of a graph G are defined as M1(G)=∑v∈VdG(v)2 and M2(G)=∑uv∈E(G)dG(u)dG(v), where dG(v) is the degree of the vertex v of graph G. Recently, Furtula et al. (2014) studied the difference between the Zagreb indices and mentioned a problem to characterize the graphs for which M1(G)>M2(G) or M1(G)2(G) or M1(G)=M2(G). In this paper we completely solve this problem.

KW - First Zagreb index

KW - Graph

KW - Second Zagreb index

UR - https://www.scopus.com/pages/publications/84991030275

U2 - 10.1016/j.dam.2016.07.008

DO - 10.1016/j.dam.2016.07.008

M3 - Article

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SN - 0166-218X

VL - 215

SP - 146

EP - 154

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

ER -

Complete characterization of graphs for direct comparing Zagreb indices

Abstract

Keywords

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