Name
Title | ||
|---|---|---|
Relating the total domination number and the annihilation number for quasi-trees and some composite graphs |
Abstract | ||
|---|---|---|
The total domination number gamma t(G) of a graph G is the cardinality of a smallest set D subset of V (G) such that each vertex of G has a neighbor in D. The annihilation number a(G) of G is the largest integer k such that there exist k different vertices in G with the degree sum at most m(G). It is conjectured that gamma t(G) <= a(G) + 1 holds for every nontrivial connected graph G. The conjecture has been proved for graphs with minimum degree at least 3, trees, certain tree-like graphs, block graphs, and cactus graphs. In the main result of this paper it is proved that the conjecture holds for quasi-trees. The conjecture is verified also for some graph constructions including bijection graphs, Mycielskians, and the newly introduced universally-identifying graphs. (C) 2022 Elsevier B.V. All rights reserved. |
Year | DOI | Venue |
|---|---|---|
2022 | 10.1016/j.disc.2022.112965 | DISCRETE MATHEMATICS |
Keywords | DocType | Volume |
Total domination number, Annihilation number, Quasi-trees, Bijection graph, Mycielskian | Journal | 345 |
Issue | ISSN | Citations |
9 | 0012-365X | 0 |
PageRank | References | Authors |
0.34 | 0 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Hongbo Hua | 1 | 54 | 10.52 |
| Xinying Hua | 2 | 0 | 0.34 |
| Sandi Klavžar | 3 | 738 | 84.46 |
| Kexiang Xu | 4 | 72 | 11.43 |