# Fractional domination in prisms

Discussiones Mathematicae Graph Theory (2007)

- Volume: 27, Issue: 3, page 541-547
- ISSN: 2083-5892

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topMatthew Walsh. "Fractional domination in prisms." Discussiones Mathematicae Graph Theory 27.3 (2007): 541-547. <http://eudml.org/doc/270624>.

@article{MatthewWalsh2007,

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 $γ_f(G×K₂) > γ_f(G)$.},

author = {Matthew Walsh},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {fractional domination; graph products; prisms of graphs},

language = {eng},

number = {3},

pages = {541-547},

title = {Fractional domination in prisms},

url = {http://eudml.org/doc/270624},

volume = {27},

year = {2007},

}

TY - JOUR

AU - Matthew Walsh

TI - Fractional domination in prisms

JO - Discussiones Mathematicae Graph Theory

PY - 2007

VL - 27

IS - 3

SP - 541

EP - 547

AB - 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 $γ_f(G×K₂) > γ_f(G)$.

LA - eng

KW - fractional domination; graph products; prisms of graphs

UR - http://eudml.org/doc/270624

ER -

## References

top- [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. Zbl1064.05111
- [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). Zbl0890.05002
- [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. Zbl1215.05092