# Weak roman domination in graphs

P. Roushini Leely Pushpam; T.N.M. Malini Mai

Discussiones Mathematicae Graph Theory (2011)

- Volume: 31, Issue: 1, page 161-170
- ISSN: 2083-5892

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topP. Roushini Leely Pushpam, and T.N.M. Malini Mai. "Weak roman domination in graphs." Discussiones Mathematicae Graph Theory 31.1 (2011): 161-170. <http://eudml.org/doc/270829>.

@article{P2011,

abstract = {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.},

author = {P. Roushini Leely Pushpam, T.N.M. Malini Mai},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {domination number; weak Roman domination number},

language = {eng},

number = {1},

pages = {161-170},

title = {Weak roman domination in graphs},

url = {http://eudml.org/doc/270829},

volume = {31},

year = {2011},

}

TY - JOUR

AU - P. Roushini Leely Pushpam

AU - T.N.M. Malini Mai

TI - Weak roman domination in graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2011

VL - 31

IS - 1

SP - 161

EP - 170

AB - 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.

LA - eng

KW - domination number; weak Roman domination number

UR - http://eudml.org/doc/270829

ER -

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