Trees with the maximal value of Graovac-Pisanski index

被引：11

作者：

Knor, Martin ^{[1
]}

Skrekovski, Riste ^{[2
,4
,5
]}

Tepeh, Aleksandra ^{[2
,3
]}

机构：

[1] Slovak Univ Technol Bratislava, Fac Civil Engn, Dept Math, Radlinskeho 11, Bratislava 81368, Slovakia

[2] Fac Informat Studies, Ljubljana 8000, Novo Mesto, Slovenia

[3] Univ Maribor, Fac Elect Engn & Comp Sci, KoroSka Cesta 46, SLO-2000 Maribor, Slovenia

[4] Univ Ljubljana, Fac Math & Phys, Ljubljana 1000, Slovenia

[5] Univ Primorska, FAMNIT, Koper 6000, Slovenia

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2019年 / 358卷

关键词：

Topological indices; Graovac-Pisanski index; Trees; MODIFIED WIENER INDEX; SYMMETRY;

D O I：

10.1016/j.amc.2019.04.034

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let G be a graph. The Graovac-Pisanski index is defined as GP(G) = vertical bar V(G)/2 vertical bar Aut(G)vertical bar Sigma(u is an element of V(G) ) Sigma(alpha is an element of Aut(G)) d(G) (u, alpha(u)), where Aut(G) is the group of automorphisms of G. This index is considered to be an extension of the original Wiener index, since it takes into account not only the distances, but also the symmetries of the graph. In this paper, for each n we find all trees on n vertices with the maximal value of Graovac-Pisanski index. With the exception of several small values of n, there are exactly two extremal trees, one of them being the path. (C) 2019 Elsevier Inc. All rights reserved.

引用

页码：287 / 292

页数：6

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