On the Wiener Index of Graphs

被引：13

作者：

Wu, Xiaoying ^{[1
]}

Liu, Huiqing ^{[1
,2
]}

机构：

[1] Hubei Univ, Sch Math & Comp Sci, Wuhan 430062, Peoples R China

[2] Hubei Univ, Hubei Key Lab Appl Math, Wuhan 430062, Peoples R China

来源：

ACTA APPLICANDAE MATHEMATICAE | 2010年 / 110卷 / 02期

关键词：

Graph; Wiener index; Cut-edge; TREES;

D O I：

10.1007/s10440-009-9460-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The Wiener index of a graph G is defined as W(G)=a (u,v) d (G) (u,v), where d (G) (u,v) is the distance between u and v in G and the sum goes over all the pairs of vertices. In this paper, we first present the 6 graphs with the first to the sixth smallest Wiener index among all graphs with n vertices and k cut edges and containing a complete subgraph of order n-k; and then we construct a graph with its Wiener index no less than some integer among all graphs with n vertices and k cut edges.

引用

页码：535 / 544

页数：10

共 18 条

[1]

Ashrafi AR, 2007, MATCH-COMMUN MATH CO, V57, P403

[2]

Bondy J. A., 1976, Graduate Texts in Mathematics, V290

[3]

Cai XC, 2008, MATCH-COMMUN MATH CO, V60, P95

[4]

Deng HY, 2007, MATCH-COMMUN MATH CO, V57, P393

[5] Wiener index of hexagonal systems [J].

Dobrynin, AA ;

Gutman, I ;

Klavzar, S ;

Zigert, P .

ACTA APPLICANDAE MATHEMATICAE, 2002, 72 (03) :247-294

[6] Wiener index of trees: Theory and applications [J].

Dobrynin, AA ;

Entringer, R ;

Gutman, I .

ACTA APPLICANDAE MATHEMATICAE, 2001, 66 (03) :211-249

[7]

GUTMAN I, 1993, INDIAN J CHEM A, V32, P651

[8]

Gutman I., 1986, Mathematical concepts in organic chemistry, DOI 10.1515/9783112570180

[9]

Liu HQ, 2008, MATCH-COMMUN MATH CO, V60, P85

[10]

Liu HQ, 2007, MATCH-COMMUN MATH CO, V58, P183

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