Weak roman domination in graphs
P. Roushini Leely Pushpam ; T.N.M. Malini Mai
Discussiones Mathematicae Graph Theory, Tome 31 (2011), p. 161-170 / Harvested from The Polish Digital Mathematics Library
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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∈Vf(v). The weak Roman domination number, denoted by γr(G), is the minimum weight of a WRDF in G. In this paper, we characterize the class of trees and split graphs for which γr(G)=γ(G) and find γr-value for a caterpillar, a 2×n grid graph and a complete binary tree.

Publié le : 2011-01-01
EUDML-ID : urn:eudml:doc:270829 
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P. Roushini Leely Pushpam; T.N.M. Malini Mai. Weak roman domination in graphs. Discussiones Mathematicae Graph Theory, Tome 31 (2011) pp. 161-170. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1532/

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