ArticleOriginal scientific text

Title

Fractional domination in prisms

Authors 1

Affiliations

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

Abstract

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 γf(G×K)>γf(G).

Keywords

fractional domination, graph products, prisms of graphs

Bibliography

  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.
Pages:
541-547
Main language of publication
English
Received
2006-09-28
Accepted
2007-04-24
Published
2007
Exact and natural sciences