On interval transmission irregular graphs
Salem Al-Yakoob, Dragan Stevanovic
TL;DR
This paper investigates the properties of interval transmission irregular graphs, proving the existence of infinite families of such graphs and expanding understanding of their structural characteristics.
Contribution
The paper provides a positive answer to whether infinite families of interval transmission irregular graphs exist, addressing a question posed by Dobrynin.
Findings
Established the existence of infinite families of ITI graphs
Characterized properties of transmission irregular graphs
Extended theoretical understanding of graph transmission sequences
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.
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