Name
Abstract | ||
|---|---|---|
The transmission of a vertex v of a graph G is the sum of distances from v to all the other vertices in G. A graph is transmission irregular if all of its vertices have pairwise different transmissions. A starlike tree T(k(1), ..., k(t)) is a tree obtained by attaching to an isolated vertex t pendant paths of lengths k(1), ..., k(t), respectively. It is proved that if a starlike tree T(a, a + 1, ..., a + k), k >= 2, is of odd order, then it is transmission irregular. T(1, 2, ..., l) l >= 3, is transmission irregular if and only if l is not an element of {r(2)+1 : r >= 2}. Additional infinite families among the starlike trees and bi-starlike trees are determined. Transmission irregular unicyclic infinite families are also presented, in particular, the line graph of T(a, a + 1, a + 2), a >= 2, is transmission irregular if and only if a is even. (C) 2020 Elsevier B.V. All rights reserved. |
Year | DOI | Venue |
|---|---|---|
2021 | 10.1016/j.dam.2020.10.025 | DISCRETE APPLIED MATHEMATICS |
Keywords | DocType | Volume |
Graph distance, Wiener complexity, Transmission irregular graphs, Starlike trees | Journal | 289 |
ISSN | Citations | PageRank |
0166-218X | 0 | 0.34 |
References | Authors | |
0 | 2 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Kexiang Xu | 1 | 72 | 11.43 |
| Sandi Klavar | 2 | 156 | 18.52 |