Sharp lower bounds for the Zagreb indices of unicyclic graphs

Batmend Horoldagva; Kinkar Ch Das

doi:10.3906/mat-1205-44

Sharp lower bounds for the Zagreb indices of unicyclic graphs

Batmend Horoldagva, Kinkar Ch Das

Department of Mathematics

Mongolian National University of Education

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

17 Scopus citations

Abstract

The first Zagreb index M₁ is equal to the sum of the squares of the degrees of the vertices, and the second Zagreb index M₂ is equal to the sum of the products of the degrees of pairs of adjacent vertices of the respective graph. In this paper we present the lower bound on M₁ and M₂ among all unicyclic graphs of given order, maximum degree, and cycle length, and characterize graphs for which the bound is attained. Moreover, we obtain some relations between the Zagreb indices for unicyclic graphs.

Original language	English
Pages (from-to)	595-603
Number of pages	9
Journal	Turkish Journal of Mathematics
Volume	39
Issue number	5
DOIs	https://doi.org/10.3906/mat-1205-44
State	Published - 2015

Keywords

Cycle length
First zagreb index
Maximum degree
Second zagreb index
Unicyclic graph

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10.3906/mat-1205-44

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title = "Sharp lower bounds for the Zagreb indices of unicyclic graphs",

abstract = "The first Zagreb index M1 is equal to the sum of the squares of the degrees of the vertices, and the second Zagreb index M2 is equal to the sum of the products of the degrees of pairs of adjacent vertices of the respective graph. In this paper we present the lower bound on M1 and M2 among all unicyclic graphs of given order, maximum degree, and cycle length, and characterize graphs for which the bound is attained. Moreover, we obtain some relations between the Zagreb indices for unicyclic graphs.",

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AU - Horoldagva, Batmend

AU - Das, Kinkar Ch

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PY - 2015

Y1 - 2015

N2 - The first Zagreb index M1 is equal to the sum of the squares of the degrees of the vertices, and the second Zagreb index M2 is equal to the sum of the products of the degrees of pairs of adjacent vertices of the respective graph. In this paper we present the lower bound on M1 and M2 among all unicyclic graphs of given order, maximum degree, and cycle length, and characterize graphs for which the bound is attained. Moreover, we obtain some relations between the Zagreb indices for unicyclic graphs.

AB - The first Zagreb index M1 is equal to the sum of the squares of the degrees of the vertices, and the second Zagreb index M2 is equal to the sum of the products of the degrees of pairs of adjacent vertices of the respective graph. In this paper we present the lower bound on M1 and M2 among all unicyclic graphs of given order, maximum degree, and cycle length, and characterize graphs for which the bound is attained. Moreover, we obtain some relations between the Zagreb indices for unicyclic graphs.

KW - Cycle length

KW - First zagreb index

KW - Maximum degree

KW - Second zagreb index

KW - Unicyclic graph

UR - https://www.scopus.com/pages/publications/84941131593

U2 - 10.3906/mat-1205-44

DO - 10.3906/mat-1205-44

M3 - Article

AN - SCOPUS:84941131593

SN - 1300-0098

VL - 39

SP - 595

EP - 603

JO - Turkish Journal of Mathematics

JF - Turkish Journal of Mathematics

IS - 5

ER -

Sharp lower bounds for the Zagreb indices of unicyclic graphs

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Keywords

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