Fractional domination in prisms

• Autorzy: Matthew Walsh
• Języki publikacji: EN

Abstrakty

EN

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 $γ_f(G×K₂) > γ_f(G)$.

Słowa kluczowe

EN

fractional domination; graph products; prisms of graphs

Kategorie tematyczne

• 05C69: Dominating sets, independent sets, cliques

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2007
• Tom: 27
• Numer: 3
• Strony: 541-547

Daty

wydano

2007

otrzymano

2006-09-28

poprawiono

2007-04-24

zaakceptowano

2007-04-25

Twórcy

autor

Matthew Walsh

• Department of Mathematical Sciences, Indiana-Purdue University, Fort Wayne, Indiana 46805, USA

Bibliografia

• [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.

Identyfikatory

DOI

10.7151/dmgt.1378