# Fractional global domination in graphs

Subramanian Arumugam; Kalimuthu Karuppasamy; Ismail Sahul Hamid

Discussiones Mathematicae Graph Theory (2010)

- Volume: 30, Issue: 1, page 33-44
- ISSN: 2083-5892

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topSubramanian Arumugam, Kalimuthu Karuppasamy, and Ismail Sahul Hamid. "Fractional global domination in graphs." Discussiones Mathematicae Graph Theory 30.1 (2010): 33-44. <http://eudml.org/doc/270977>.

@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 -

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