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.
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