Direct Comparison of the Variable Zagreb Indices of Cyclic Graphs

Tsend Ayush Selenge; Batmend Horoldagva; Kinkar Ch Das

Direct Comparison of the Variable Zagreb Indices of Cyclic Graphs

Tsend Ayush Selenge, Batmend Horoldagva, Kinkar Ch Das

Department of Mathematics

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

11 Scopus citations

Abstract

Given a graph G = (V, E), the variable first and second Zagreb indices are defined by ^λM₁(G) = ^P_vi∈V d²_i^λ and ^λM₂(G) = ^P_vi_vj∈E d^λ_i · d^λ_j , where d_i is the degree of the vertex v_i and λ is any real number. Let G_ν be the class of connected graphs with cyclomatic number ν (ν ≥ 1). In this paper, we give a lower bound on ^λM₂(G) − ^λM₁(G) in terms of ν and λ in G_ν for all λ ∈ (0, 1] and characterize the extremal graphs.

Original language	English
Pages (from-to)	351-360
Number of pages	10
Journal	Match
Volume	78
Issue number	2
State	Published - 2017

Cite this

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title = "Direct Comparison of the Variable Zagreb Indices of Cyclic Graphs",

abstract = "Given a graph G = (V, E), the variable first and second Zagreb indices are defined by λM1(G) = Pvi∈V d2iλ and λM2(G) = Pvivj∈E dλi · dλj , where di is the degree of the vertex vi and λ is any real number. Let Gν be the class of connected graphs with cyclomatic number ν (ν ≥ 1). In this paper, we give a lower bound on λM2(G) − λM1(G) in terms of ν and λ in Gν for all λ ∈ (0, 1] and characterize the extremal graphs.",

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

year = "2017",

language = "English",

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pages = "351--360",

journal = "Match",

issn = "0340-6253",

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AU - Selenge, Tsend Ayush

AU - Horoldagva, Batmend

AU - Das, Kinkar Ch

PY - 2017

Y1 - 2017

N2 - Given a graph G = (V, E), the variable first and second Zagreb indices are defined by λM1(G) = Pvi∈V d2iλ and λM2(G) = Pvivj∈E dλi · dλj , where di is the degree of the vertex vi and λ is any real number. Let Gν be the class of connected graphs with cyclomatic number ν (ν ≥ 1). In this paper, we give a lower bound on λM2(G) − λM1(G) in terms of ν and λ in Gν for all λ ∈ (0, 1] and characterize the extremal graphs.

AB - Given a graph G = (V, E), the variable first and second Zagreb indices are defined by λM1(G) = Pvi∈V d2iλ and λM2(G) = Pvivj∈E dλi · dλj , where di is the degree of the vertex vi and λ is any real number. Let Gν be the class of connected graphs with cyclomatic number ν (ν ≥ 1). In this paper, we give a lower bound on λM2(G) − λM1(G) in terms of ν and λ in Gν for all λ ∈ (0, 1] and characterize the extremal graphs.

UR - https://www.scopus.com/pages/publications/85061794374

M3 - Article

AN - SCOPUS:85061794374

SN - 0340-6253

VL - 78

SP - 351

EP - 360

JO - Match

JF - Match

IS - 2

ER -

Direct Comparison of the Variable Zagreb Indices of Cyclic Graphs

Abstract

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