Infinite family of 3-connected cubic transmission irregular graphs

被引：15

作者：

Dobrynin, Andrey A. ^{[1
,2
]}

机构：

[1] Novosibirsk State Univ, Novosibirsk 630090, Russia

[2] Russian Acad Sci, Siberian Branch, Sobolev Inst Math, Novosibirsk 630090, Russia

来源：

DISCRETE APPLIED MATHEMATICS | 2019年 / 257卷

关键词：

Graph invariant; Vertex transmission; Transmission irregular graph; Wiener complexity; WIENER INDEX; COMPLEXITY; TREES;

D O I：

10.1016/j.dam.2018.10.036

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Distance between two vertices is the number of edges in a shortest path connecting them in a connected graph G. The transmission of a vertex v is the sum of distances from v to all the other vertices of G. If transmissions of all vertices are mutually distinct, then G is a transmission irregular graph. It is known that almost no graphs are transmission irregular. Infinite families of transmission irregular trees and 2-connected graphs were presented in Alizadeh and Klavzar (2018) and Dobrynin (2019) [8, 9]. The following problem was posed in Alizadeh and Klavzar (2018): do there exist infinite families of regular transmission irregular graphs? In this paper, an infinite family of 3-connected cubic transmission irregular graphs is constructed. (C) 2018 Elsevier B.V. All rights reserved.

引用

页码：151 / 157

页数：7