On the extremal values of the eccentric distance sum of trees with a given maximum degree

被引：3

作者：

Miao, Lianying ^{[1
]}

Pang, Jingru ^{[2
]}

Xu, Shoujun ^{[3
]}

机构：

[1] China Univ Min & Technol, Sch Math, Xuzhou 221008, Jiangsu, Peoples R China

[2] Dalian Univ Technol, Sch Energy & Power, Dalian 116024, Peoples R China

[3] Lanzhou Univ, Sch Math & Stat, Gansu Key Lab Appl Math & Complex Syst, Lanzhou 730000, Gansu, Peoples R China

来源：

DISCRETE APPLIED MATHEMATICS | 2020年 / 284卷

基金：

中国国家自然科学基金;

关键词：

Tree; Eccentric distance sum; Maximum degree; CONNECTIVITY INDEX; DEGREE SEQUENCE; WIENER INDEX; GRAPHS; INVARIANT;

D O I：

10.1016/j.dam.2020.03.059

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let G be a simple connected graph. The eccentric distance sum (EDS) of G is defined as xi(d)(G) = Sigma(v is an element of V)epsilon(G)(v)D-G(v)D-G(v), where epsilon(G)(v) is the eccentricity of the vertex v and D-G(v) = Sigma(u)(is an element of V)d(G)(u, v) is the sum of all distances from the vertex v. In this paper, the extremal tree which minimizes the EDS among n-vertex trees of given maximum degree is characterized. This proves Conjecture 3.2 posed in Miao et al., (2015). (C) 2020 Elsevier B.V. All rights reserved.

引用

页码：375 / 383

页数：9

共 28 条

[1] Extremal graphs for inequalities involving domination parameters [J].

Baogen, X ;

Cockayne, EJ ;

Haynes, TW ;

Hedetniemi, ST ;

Shangchao, Z .

DISCRETE MATHEMATICS, 2000, 216 (1-3) :1-10

[2] Connectivity, diameter, minimal degree, independence number and the eccentric distance sum of graphs [J].

Chen, Shuya ;

Li, Shuchao ;

Wu, Yueyu ;

Sun, Lingli .

DISCRETE APPLIED MATHEMATICS, 2018, 247 :135-146

[3] Closed formulas for the numbers of small independent sets and matchings and an extremal problem for trees [J].

Delorme, C ;

Favaron, O ;

Rautenbach, D .

DISCRETE APPLIED MATHEMATICS, 2003, 130 (03) :503-512

[4] Wiener index versus maximum degree in trees [J].

Fischermann, M ;

Hoffmann, A ;

Rautenbach, D ;

Székely, L ;

Volkmann, L .

DISCRETE APPLIED MATHEMATICS, 2002, 122 (1-3) :127-137

[5] Extremal values on the eccentric distance sum of trees [J].

Geng, Xianya ;

Li, Shuchao ;

Zhang, Meng .

DISCRETE APPLIED MATHEMATICS, 2013, 161 (16-17) :2427-2439

[6] Eccentric distance sum: A novel graph invariant for predicting biological and physical properties [J].

Gupta, S ;

Singh, M ;

Madan, AK .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2002, 275 (01) :386-401

[7] Further results on the eccentric distance sum [J].

Hua, Hongbo ;

Zhang, Shenggui ;

Xu, Kexiang .

DISCRETE APPLIED MATHEMATICS, 2012, 160 (1-2) :170-180

[8] A short and unified proof of Yu et al.'s two results on the eccentric distance sum [J].

Hua, Hongbo ;

Xu, Kexiang ;

Wen, Shu .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2011, 382 (01) :364-366

[9]

Ilic A, 2011, MATCH-COMMUN MATH CO, V65, P731

[10] On the eccentric distance sum of graphs [J].

Ilic, Aleksandar ;

Yu, Guihai ;

Feng, Lihua .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2011, 381 (02) :590-600

← 1 2 3 →