- Tytuł:
- Weak roman domination in graphs
- Autorzy:
-
Roushini Leely Pushpam, P.
Malini Mai, T. - Powiązania:
- https://bibliotekanauki.pl/articles/743835.pdf
- Data publikacji:
- 2011
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
domination number
weak Roman domination number - Opis:
- Let G = (V,E) be a graph and f be a function f:V → {0,1,2}. A vertex u with f(u) = 0 is said to be undefended with respect to f, if it is not adjacent to a vertex with positive weight. The function f is a weak Roman dominating function (WRDF) if each vertex u with f(u) = 0 is adjacent to a vertex v with f(v) > 0 such that the function f': V → {0,1,2} defined by f'(u) = 1, f'(v) = f(v)-1 and f'(w) = f(w) if w ∈ V-{u,v}, has no undefended vertex. The weight of f is $w(f) = ∑_{v ∈ V}f(v)$. The weak Roman domination number, denoted by $γ_r(G)$, is the minimum weight of a WRDF in G. In this paper, we characterize the class of trees and split graphs for which $γ_r(G) = γ(G)$ and find $γ_r$-value for a caterpillar, a 2×n grid graph and a complete binary tree.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2011, 31, 1; 161-170
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł