Name
Abstract | ||
|---|---|---|
Let k >= 1 be an integer and G be a simple and finite graph with vertex set V(G). A signed double Roman k-dominating function (SDRkDF) on a graph G is a function f : V(G) -> {-1, 1, 2, 3} such that (i) every vertex v with f(v) = -1 is adjacent to at least two vertices assigned a 2 or to at least one vertex w with f(w) = 3; (ii) every vertex v with f(v) = 1 is adjacent to at least one vertex w with f(w) >= 2 and (iii) Sigma(u is an element of N[v])f(u) >= k holds for any vertex v. The weight of a SDRkDF f is Sigma(u is an element of V(G))f(u), and the minimum weight of a SDRkDF is the signed double Roman k-domination number gamma(k)(sdR)(G) of G. In this paper, we investigate the signed double Roman k-domination number of trees. In particular, we present lower and upper bounds on gamma(k)(sdR)(T) for 2 <= k <= 6 and classify all extremal trees. |
Year | DOI | Venue |
|---|---|---|
2019 | 10.1051/ro/2018043 | RAIRO-OPERATIONS RESEARCH |
Keywords | DocType | Volume |
Signed double Roman k-dominating function,signed double Roman k-domination number | Journal | 53 |
Issue | ISSN | Citations |
2 | 0399-0559 | 0 |
PageRank | References | Authors |
0.34 | 0 | 7 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Hong Yang | 1 | 0 | 1.35 |
| Pu Wu | 2 | 2 | 2.79 |
| Sakineh Nazari-Moghaddam | 3 | 0 | 0.34 |
| Seyed Mahmoud Sheikholeslami | 4 | 54 | 28.15 |
| Xiao-song Zhang | 5 | 305 | 45.10 |
| Zehui Shao | 6 | 119 | 30.98 |
| Yuan Yan Tang | 7 | 2662 | 209.20 |