Characterization of transmission irregular starlike and double starlike trees
Combinatorics
2025-06-09 v1
Abstract
The transmission of a vertex in a connected graph is the sum of its distances to all the other vertices. A graph is transmission irregular (TI) when all of its vertices have mutually distinct transmissions. In an earlier paper, Al-Yakoob and Stevanovi\'c [Appl. Math. Comput. 380 (2020), 125257] gave the full characterization of TI starlike trees with three branches. Here, we improve these results by using a different approach to provide the complete characterization of all TI starlike trees. Moreover, we find the precise conditions under which a double starlike tree is TI. Finally, we implement the aforementioned conditions in order to find several infinite families of TI starlike trees and TI double starlike trees.
Keywords
Cite
@article{arxiv.2311.14259,
title = {Characterization of transmission irregular starlike and double starlike trees},
author = {Ivan Damnjanović},
journal= {arXiv preprint arXiv:2311.14259},
year = {2025}
}