Name
Abstract | ||
|---|---|---|
The semitotal domination number of a graph G without isolated vertices is the minimum cardinality of a set S of vertices of G such that every vertex in \(V(G){\setminus } S\) is adjacent to at least one vertex in S, and every vertex in S is within distance 2 of another vertex of S. In Henning and Marcon (Ann Comb 20(4):1–15, 2016), it was shown that every connected claw-free cubic graph G of order n has semitotal domination number at most \(\frac{4n}{11}\) when \(n\ge 10\), and it was conjectured that the bound can be improved from \(\frac{4n}{11}\) to \(\frac{n}{3}\) if \(G\notin \{K_4,N_2\}\). In this paper, we prove this conjecture. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1007/s00373-017-1826-z | Graphs and Combinatorics |
Keywords | Field | DocType |
Cubic graph, Semitotal domination, Claw-free | Discrete mathematics,Graph,Combinatorics,Dominating set,Vertex (geometry),Cubic graph,Cardinality,Induced subgraph,Domination analysis,Mathematics | Journal |
Volume | Issue | ISSN |
33 | 5 | 0911-0119 |
Citations | PageRank | References |
6 | 0.63 | 14 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Enqiang Zhu | 1 | 25 | 11.99 |
| Zehui Shao | 2 | 119 | 30.98 |
| Jin Xu | 3 | 230 | 45.13 |