Infinite family of 2-connected transmission irregular graphs

Andrey A. Dobrynin

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

Abstract

Distance between two vertices is the number of edges in the 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 were presented in [4]. The following problem was posed in [4]: do there exist infinite families of 2-connected transmission irregular graphs? In this paper, an infinite family of such graphs is constructed.

Original languageEnglish
Pages (from-to)1-4
Number of pages4
JournalApplied Mathematics and Computation
Volume340
DOIs
Publication statusPublished - 1 Jan 2019

Keywords

  • Transmission irregular graph
  • Vertex transmission
  • Wiener complexity
  • TREES
  • WIENER INDEX
  • COMPLEXITY
  • TOPOLOGICAL INDEXES

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