English

On interval transmission irregular graphs

Combinatorics 2020-10-22 v1

Abstract

Transmission of a vertex v of a connected graph G is the sum of distances from v to all other vertices in G. Graph G is transmission irregular (TI) if no two of its vertices have the same transmission, and G is interval transmission irregular (ITI) if it is TI and the vertex transmissions of G form a sequence of consecutive integers. Here we give a positive answer to the question of Dobrynin [Appl Math Comput 340 (2019), 1-4] of whether infinite families of ITI graphs exist.

Keywords

Cite

@article{arxiv.2010.11014,
  title  = {On interval transmission irregular graphs},
  author = {Salem Al-Yakoob and Dragan Stevanovic},
  journal= {arXiv preprint arXiv:2010.11014},
  year   = {2020}
}

Comments

19pp, 15 figures

R2 v1 2026-06-23T19:31:25.172Z