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.
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页码：151 / 157
页数：7
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