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

• [1] S. Arumugam and R. Kala, A note on global domination in graphs, Ars Combin. 93 (2009) 175-180.
• [2] S. Arumugam and K. Rejikumar, Basic minimal dominating functions, Utilitas Mathematica 77 (2008) 235-247.
• [3] G. Chartrand and L. Lesniak, Graphs & Digraphs (Fourth Edition, Chapman & Hall/CRC, 2005).
• [4] E.J. Cockayne, G. MacGillivray and C.M. Mynhardt, Convexity of minimal dominating funcitons of trees-II, Discrete Math. 125 (1994) 137-146, doi: 10.1016/0012-365X(94)90154-6.
• [5] E.J. Cockayne, C.M. Mynhardt and B. Yu, Universal minimal total dominating functions in graphs, Networks 24 (1994) 83-90, doi: 10.1002/net.3230240205.
• [6] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, Inc., 1998).
• [7] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Domination in Graphs: Advanced Topics (Marcel Dekker, Inc., 1998).
• [8] S.M. Hedetniemi, S.T. Hedetniemi and T.V. Wimer, Linear time resource allocation algorithms for trees, Technical report URI -014, Department of Mathematics, Clemson University (1987).
• [9] E. Sampathkumar, The global domination number of a graph, J. Math. Phys. Sci. 23 (1989) 377-385.
• [10] E.R. Scheinerman and D.H. Ullman, Fractional Graph Theory: A Rational Approch to the Theory of Graphs (John Wiley & Sons, New York, 1997).

Identyfikatory

DOI

10.7151/dmgt.1474