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 .
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1378,
author = {Matthew Walsh},
title = {Fractional domination in prisms},
journal = {Discussiones Mathematicae Graph Theory},
volume = {27},
year = {2007},
pages = {541-547},
zbl = {1142.05063},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1378}
}
Matthew Walsh. Fractional domination in prisms. Discussiones Mathematicae Graph Theory, Tome 27 (2007) pp. 541-547. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1378/
[000] [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. | Zbl 1064.05111
[001] [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.
[002] [3] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, Inc., New York, 1998). | Zbl 0890.05002
[003] [4] C.M. Mynhardt, A conjecture on domination in prisms of graphs, presented at the Ottawa-Carleton Discrete Math Day 2006, Ottawa, Ontario, Canada.
[004] [5] R.R. Rubalcaba and M. Walsh, Minimum fractional dominating functions and maximum fractional packing functions, in preparation. | Zbl 1215.05092