Sharp lower bounds for the Zagreb indices of unicyclic graphs

被引：17

作者：

Horoldagva, Batmend ^{[1
]}

Das, Kinkar Ch. ^{[2
]}

机构：

[1] Mongolian State Univ Educ, Sch Math & Stat, Ulaanbaatar, Mongolia

[2] Sungkyunkwan Univ, Dept Math, Suwon, South Korea

来源：

TURKISH JOURNAL OF MATHEMATICS | 2015年 / 39卷 / 05期

基金：

新加坡国家研究基金会;

关键词：

First Zagreb index; second Zagreb index; unicyclic graph; maximum degree; cycle length; MOLECULAR-ORBITALS;

D O I：

10.3906/mat-1205-44

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The first Zagreb index M-1 is equal to the sum of the squares of the degrees of the vertices, and the second Zagreb index M-2 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 M-1 and M-2 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.

引用

页码：595 / 603

页数：9

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