Fractional global domination in graphs

• Autorzy: Subramanian Arumugam , Kalimuthu Karuppasamy , Ismail Sahul Hamid
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

domination; global domination; dominating function; global dominating function; fractional global domination number

Kategorie tematyczne

• 05C69: Dominating sets, independent sets, cliques

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2010
• Tom: 30
• Numer: 1
• Strony: 33-44

Daty

wydano

2010

otrzymano

2008-09-19

poprawiono

2009-01-12

zaakceptowano

2009-01-12

Twórcy

autor

Subramanian Arumugam

• Core Group Research Facility (CGRF), National Centre for Advanced Research in Discrete Mathematics, (n-CARDMATH), Kalasalingam University, Anand Nagar, Krishnankoil-626 190, India

autor

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

autor

Ismail Sahul Hamid

• Department of Mathematics, The Madura College, Madurai-625 011, India

Bibliografia

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• [7] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Domination in Graphs: Advanced Topics (Marcel Dekker, Inc., 1998).
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Identyfikatory

DOI

10.7151/dmgt.1474