Name
Abstract | ||
|---|---|---|
Let G=(V,E) be a graph, a function g:E→{-1,1} is said to be a signed cycle dominating function (SCDF for short) of G if Σ eεE(C) g(e)≥1 holds for any induced cycle C of G. The signed cycle domination number of G is defined as γ sc (G)=min{Σ eεE(G) g(e)â̂£g is an SCDF of G}. Xu (Discrete Math. 309:1007-1012, 2009) first researched the signed cycle domination number of graphs and raised the following conjectures: (1) Let G be a maximal planar graphs of order n≥3. Then γ sc (G)=n-2; (2) For any graph G with δ(G)=3, γ sc (G)≥1; (3) For any 2-connected graph G, γ sc (G)≥1. In this paper, we present some results about these conjectures. © 2012 Springer Science+Business Media, LLC. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1007/s10878-012-9506-7 | J. Comb. Optim. |
Keywords | Field | DocType |
Domination number,Signed cycle domination number,Planar graph,Maximal planar graph | Graph,Discrete mathematics,Combinatorics,Graph power,Bound graph,Domination analysis,Planar graph,Mathematics | Journal |
Volume | Issue | ISSN |
25 | 4 | 15732886 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| GUAN Jian | 1 | 47 | 15.77 |
| Xiaoyan Liu | 2 | 0 | 0.34 |
| Changhong Lu | 3 | 123 | 13.30 |
| Zhengke Miao | 4 | 66 | 17.62 |