Geodesic
Fractional global domination in graphs
Discussiones Mathematicae. Graph Theory, Tome 30 (2010) no. 1, pp. 33-44.

Voir la notice de l'article provenant de la source Library of Science

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 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.
Keywords: domination, global domination, dominating function, global dominating function, fractional global domination number 
@article{DMGT_2010_30_1_a2,
     author = {Arumugam, Subramanian and Karuppasamy, Kalimuthu and Hamid, Ismail},
     title = {Fractional global domination in graphs},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {33--44},
     publisher = {mathdoc},
     volume = {30},
     number = {1},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2010_30_1_a2/}
}
TY  - JOUR
AU  - Arumugam, Subramanian
AU  - Karuppasamy, Kalimuthu
AU  - Hamid, Ismail
TI  - Fractional global domination in graphs
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2010
SP  - 33
EP  - 44
VL  - 30
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2010_30_1_a2/
LA  - en
ID  - DMGT_2010_30_1_a2
ER  - 
%0 Journal Article
%A Arumugam, Subramanian
%A Karuppasamy, Kalimuthu
%A Hamid, Ismail
%T Fractional global domination in graphs
%J Discussiones Mathematicae. Graph Theory
%D 2010
%P 33-44
%V 30
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2010_30_1_a2/
%G en
%F DMGT_2010_30_1_a2
Arumugam, Subramanian; Karuppasamy, Kalimuthu; Hamid, Ismail. Fractional global domination in graphs. Discussiones Mathematicae. Graph Theory, Tome 30 (2010) no. 1, pp. 33-44. http://geodesic.mathdoc.fr/item/DMGT_2010_30_1_a2/

[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).