Some further results on the eccentric distance sum

被引:7
作者
Huang, Ziwen [1 ,2 ]
Xi, Xiaozhong [1 ,2 ]
Yuan, Shaoliang [1 ,2 ]
机构
[1] Yichun Univ, Sch Math & Comp Sci, Yichun 336000, Jiangxi, Peoples R China
[2] Yichun Univ, Ctr Appl Math, Yichun 336000, Jiangxi, Peoples R China
基金
中国国家自然科学基金;
关键词
Eccentric distance sum; Halin graph; Complement; Bipartite graph; CHROMATIC NUMBER; EXTREMAL VALUES; WIENER INDEX; GRAPHS; TREES;
D O I
10.1016/j.jmaa.2018.09.059
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Let G = (V (G), E(G)) be a simple connected graph. Then the eccentric distance sum of G, which is a novel graph invariant by offering a great potential for structure = EvEv activity/property relationships, is defined as xi(d)(G) = Sigma(nu is an element of v) epsilon G (G)DG (v), where epsilon(G) (v) is the eccentricity of the vertex v, and DG (nu) is the sum of all distance from the vertex v. As a continuation to the parts of [22] (Li et al., J. Math. Anal. Appl. 43:1149-1162, 2015), and [17] (Hua et al., Discrete Appl. Math. 160:170-180, 2012), this paper answers one of some remaining problems in [22] is how to determine the bipartite graphs of even diameter with the minimum EDS, and gives a Nordhaus-addum bound for eccentric distance sum, which is the generalization of the corresponding results in [17]. Moreover, some sharp lower bounds on the EDS of Hahn graphs, and of triangle -free and quadrangle-free graphs are respectively presented. (C) 2018 Elsevier Inc. All rights reserved.
引用
收藏
页码:145 / 158
页数:14
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