Fractional domination in prisms
Discussiones Mathematicae. Graph Theory, Tome 27 (2007) no. 3, pp. 541-547.

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

Mynhardt has conjectured that if G is a graph such that γ(G) = γ(πG) for all generalized prisms πG then G is edgeless. The fractional analogue of this conjecture is established and proved by showing that, if G is a graph with edges, then γ_f(G×K₂) > γ_f(G).
Keywords: fractional domination, graph products, prisms of graphs
@article{DMGT_2007_27_3_a9,
     author = {Walsh, Matthew},
     title = {Fractional domination in prisms},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {541--547},
     publisher = {mathdoc},
     volume = {27},
     number = {3},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2007_27_3_a9/}
}
TY  - JOUR
AU  - Walsh, Matthew
TI  - Fractional domination in prisms
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2007
SP  - 541
EP  - 547
VL  - 27
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2007_27_3_a9/
LA  - en
ID  - DMGT_2007_27_3_a9
ER  - 
%0 Journal Article
%A Walsh, Matthew
%T Fractional domination in prisms
%J Discussiones Mathematicae. Graph Theory
%D 2007
%P 541-547
%V 27
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2007_27_3_a9/
%G en
%F DMGT_2007_27_3_a9
Walsh, Matthew. Fractional domination in prisms. Discussiones Mathematicae. Graph Theory, Tome 27 (2007) no. 3, pp. 541-547. http://geodesic.mathdoc.fr/item/DMGT_2007_27_3_a9/

[1] A.P. Burger, C.M. Mynhardt and W.D. Weakley, On the domination number of prisms of graphs, Discuss. Math. Graph Theory 24 (2004) 303-318, doi: 10.7151/dmgt.1233.

[2] G. Fricke, Upper domination on double cone graphs, in: Proceedings of the Twentieth Southeastern Conference on Combinatorics, Graph Theory, and Computing (Boca Raton, FL, 1989), Congr. Numer. 72 (1990) 199-207.

[3] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, Inc., New York, 1998).

[4] C.M. Mynhardt, A conjecture on domination in prisms of graphs, presented at the Ottawa-Carleton Discrete Math Day 2006, Ottawa, Ontario, Canada.

[5] R.R. Rubalcaba and M. Walsh, Minimum fractional dominating functions and maximum fractional packing functions, in preparation.