Fractional global domination in graphs

@article{SubramanianArumugam2010,
abstract = {Let G = (V,E) be a graph. A function g:V → [0,1] is called a global dominating function (GDF) of G, if for every v ∈ V, $g(N[v]) = ∑_\{u ∈ N[v]\}g(u) ≥ 1$ and $g(\overline\{N(v)\}) = ∑_\{u ∉ N(v)\}g(u) ≥ 1$. A GDF g of a graph G is called minimal (MGDF) if for all functions f:V → [0,1] such that f ≤ g and f(v) ≠ g(v) for at least one v ∈ V, f is not a GDF. The fractional global domination number $γ_\{fg\}(G)$ is defined as follows: $γ_\{fg\}(G)$ = min|g|:g is an MGDF of G where $|g| = ∑_\{v ∈ V\} g(v)$. In this paper we initiate a study of this parameter.},
author = {Subramanian Arumugam, Kalimuthu Karuppasamy, Ismail Sahul Hamid},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {domination; global domination; dominating function; global dominating function; fractional global domination number},
language = {eng},
number = {1},
pages = {33-44},
title = {Fractional global domination in graphs},
url = {http://eudml.org/doc/270977},
volume = {30},
year = {2010},
}

TY - JOUR
AU - Subramanian Arumugam
AU - Kalimuthu Karuppasamy
AU - Ismail Sahul Hamid
TI - Fractional global domination in graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2010
VL - 30
IS - 1
SP - 33
EP - 44
AB - Let G = (V,E) be a graph. A function g:V → [0,1] is called a global dominating function (GDF) of G, if for every v ∈ V, $g(N[v]) = ∑_{u ∈ N[v]}g(u) ≥ 1$ and $g(\overline{N(v)}) = ∑_{u ∉ N(v)}g(u) ≥ 1$. A GDF g of a graph G is called minimal (MGDF) if for all functions f:V → [0,1] such that f ≤ g and f(v) ≠ g(v) for at least one v ∈ V, f is not a GDF. The fractional global domination number $γ_{fg}(G)$ is defined as follows: $γ_{fg}(G)$ = min|g|:g is an MGDF of G where $|g| = ∑_{v ∈ V} g(v)$. In this paper we initiate a study of this parameter.
LA - eng
KW - domination; global domination; dominating function; global dominating function; fractional global domination number
UR - http://eudml.org/doc/270977
ER -