On the eccentric distance sum of graphs
On the eccentric distance sum of graphs
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关于图的偏心距和
DOI：
10.1016/j.jmaa.2011.02.086
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发表时间：
2011-09-15
影响因子：
1.3
通讯作者：
Feng, Lihua
中科院分区：
文献类型：
--
作者：
Ilic, Aleksandar;Yu, Guihai;Feng, Lihua
偏心距离和是一种新颖的拓扑指数，为结构活动/性质关系提供了巨大的潜力。对于图C，它被定义为xi(d)(G) = Sigma（v是v的一个元素）epsilon(v) d(v)，其中epsilon(v)是顶点v的偏心率，d(v) = Sigma（u是v (G)的一个元素）d（u, v）是到顶点v的所有距离的和，由[G]驱动。余立峰，李建平，单环图与树的偏心距离和，数学学报。分析的。应用学报，375(2011)934-944]，本文刻画了具有最大偏心距离和的极值树和图。根据维纳指数、度距离、偏心连通性指数、独立数、连通性、匹配数、色数和团数等图不变量，建立了偏心距离和的各种下界和上界。此外，我们提出了笛卡尔积偏心距离和值的显式公式，应用于一些化学兴趣图（如纳米管和纳米环）。(C) 2011爱思唯尔公司版权所有。
The eccentric distance sum is a novel topological index that offers a vast potential for structure activity/property relationships. For a graph C, it is defined as xi(d)(G) = Sigma(v is an element of V) epsilon(v)D(v), where epsilon(v) is the eccentricity of the vertex v and D(v) = Sigma(u is an element of V(G)) d(u, v) is the sum of all distances from the vertex v. Motivated by [G. Yu, L Feng, A. Ilic, On the eccentric distance sum of trees and unicyclic graphs, J. Math. Anal. Appl. 375 (2011) 934-944], in this paper we characterize the extremal trees and graphs with maximal eccentric distance sum. Various lower and upper bounds for the eccentric distance sum in terms of other graph invariants including the Wiener index, the degree distance, eccentric connectivity index, independence number, connectivity, matching number, chromatic number and clique number are established. In addition, we present explicit formulae for the values of eccentric distance sum for the Cartesian product, applied to some graphs of chemical interest (like nanotubes and nanotori). (C) 2011 Elsevier Inc. All rights reserved.