Name
Abstract | ||
|---|---|---|
A perfect Italian dominating function (PIDF) on a graph G is a function f : V (G) -> {0, 1, 2} satisfying the condition that for every vertex u with f(u) = 0, the total weight of f assigned to the neighbors of u is exactly two. The weight of a PIDF is the sum of its functions values over all vertices. The perfect Italian domination number of G, denoted gamma(p)(I)(G), is the minimum weight of a PIDF of G. In this paper, we show that for every tree T of order n >= 3, with l(T) leaves and s(T) support vertices, gamma(p)(I)(T) <= gamma Ip(T)<= 4n-l(T)+2s(T-1)/5, improving a previous bound given by T.W. Haynes and M.A. Henning in [Perfect Italian domination in trees, Discrete Appl. Math. 260 (2019) 164-177]. |
Year | DOI | Venue |
|---|---|---|
2022 | 10.7151/dmgt.2324 | DISCUSSIONES MATHEMATICAE GRAPH THEORY |
Keywords | DocType | Volume |
Italian domination, Roman domination, perfect Italian domination | Journal | 42 |
Issue | ISSN | Citations |
3 | 1234-3099 | 0 |
PageRank | References | Authors |
0.34 | 0 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Sakineh Nazari-Moghaddam | 1 | 0 | 0.34 |
| Mustapha Chellali | 2 | 0 | 0.34 |