English

New transmission irregular chemical graphs

Combinatorics 2022-11-10 v1

Abstract

The transmission of a vertex vv of a (chemical) graph GG is the sum of distances from vv to other vertices in GG. If any two vertices of GG have different transmissions, then GG is a transmission irregular graph. It is shown that for any odd number n7n\geq 7 there exists a transmission irregular chemical tree of order nn. A construction is provided which generates new transmission irregular (chemical) trees. Two additional families of chemical graphs are characterized by property of transmission irregularity and two sufficient condition provided which guarantee that the transmission irregularity is preserved upon adding a new edge.

Keywords

Cite

@article{arxiv.2211.04836,
  title  = {New transmission irregular chemical graphs},
  author = {Kexiang Xu and Jing Tian and Sandi Klavžar},
  journal= {arXiv preprint arXiv:2211.04836},
  year   = {2022}
}
R2 v1 2026-06-28T05:30:09.789Z