Name
Abstract | ||
|---|---|---|
For a graph G with vertex set V(G) and function f:V(G)→{0,1,2,3}, let Vi be the set of vertices assigned i by f. A perfect double Roman dominating function of a graph G is a function f:V(G)→{0,1,2,3} satisfying the conditions that (i) if u∈V0, then u is either adjacent to exactly two vertices in V2 and no vertex in V3 or adjacent to exactly one vertex in V3 and no vertex in V2; and (ii) if u∈V1, then u is adjacent to exactly one vertex in V2 and no vertex in V3. The perfect double Roman domination number of G, denoted γdRp(G), is the minimum weight of a perfect double Roman dominating function of G. We prove that if T is a tree of order n≥3, then γdRp(T)≤9n∕7. In addition, we give a family of trees T of order n for which γdRp(T) approaches this upper bound as n goes to infinity. |
Year | DOI | Venue |
|---|---|---|
2020 | 10.1016/j.dam.2020.03.021 | Discrete Applied Mathematics |
Keywords | DocType | Volume |
Roman domination,Double Roman domination,Perfect double Roman domination | Journal | 284 |
ISSN | Citations | PageRank |
0166-218X | 0 | 0.34 |
References | Authors | |
0 | 2 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Ayotunde T. Egunjobi | 1 | 0 | 0.34 |
| Teresa W. Haynes | 2 | 774 | 94.22 |