Discussiones Mathematicae Graph Theory 30(1) (2010) 33-44
doi: 10.7151/dmgt.1474

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FRACTIONAL GLOBAL DOMINATION IN GRAPHS

Subramanian Arumugam, Kalimuthu Karuppasamy

Core Group Research Facility (CGRF)
National Centre for Advanced Research in Discrete Mathematics
(n-CARDMATH), Kalasalingam University
Anand Nagar, Krishnankoil-626 190, India
e-mail: s.arumugam.klu@gmail.com
k_karuppasamy@yahoo.co.in

Ismail Sahul Hamid

Department of Mathematics
The Madura College, Madurai-625 011, India
e-mail: sahulmat@yahoo.co.in

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([`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 γfg(G) is defined as follows: γfg(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.

Keywords: domination, global domination, dominating function, global dominating function, fractional global domination number.

2010 Mathematics Subject Classification: 05C69.

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Received 19 September 2008
Revised 12 January 2009
Accepted 12 January 2009