# On the domination number of prisms of graphs

• Volume: 24, Issue: 2, page 303-318
• ISSN: 2083-5892

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## Abstract

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For a permutation π of the vertex set of a graph G, the graph π G is obtained from two disjoint copies G₁ and G₂ of G by joining each v in G₁ to π(v) in G₂. Hence if π = 1, then πG = K₂×G, the prism of G. Clearly, γ(G) ≤ γ(πG) ≤ 2 γ(G). We study graphs for which γ(K₂×G) = 2γ(G), those for which γ(πG) = 2γ(G) for at least one permutation π of V(G) and those for which γ(πG) = 2γ(G) for each permutation π of V(G).

## How to cite

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Alewyn P. Burger, Christina M. Mynhardt, and William D. Weakley. "On the domination number of prisms of graphs." Discussiones Mathematicae Graph Theory 24.2 (2004): 303-318. <http://eudml.org/doc/270590>.

@article{AlewynP2004,
abstract = {For a permutation π of the vertex set of a graph G, the graph π G is obtained from two disjoint copies G₁ and G₂ of G by joining each v in G₁ to π(v) in G₂. Hence if π = 1, then πG = K₂×G, the prism of G. Clearly, γ(G) ≤ γ(πG) ≤ 2 γ(G). We study graphs for which γ(K₂×G) = 2γ(G), those for which γ(πG) = 2γ(G) for at least one permutation π of V(G) and those for which γ(πG) = 2γ(G) for each permutation π of V(G).},
author = {Alewyn P. Burger, Christina M. Mynhardt, William D. Weakley},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {domination; graph products; prisms of graphs},
language = {eng},
number = {2},
pages = {303-318},
title = {On the domination number of prisms of graphs},
url = {http://eudml.org/doc/270590},
volume = {24},
year = {2004},
}

TY - JOUR
AU - Alewyn P. Burger
AU - Christina M. Mynhardt
AU - William D. Weakley
TI - On the domination number of prisms of graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2004
VL - 24
IS - 2
SP - 303
EP - 318
AB - For a permutation π of the vertex set of a graph G, the graph π G is obtained from two disjoint copies G₁ and G₂ of G by joining each v in G₁ to π(v) in G₂. Hence if π = 1, then πG = K₂×G, the prism of G. Clearly, γ(G) ≤ γ(πG) ≤ 2 γ(G). We study graphs for which γ(K₂×G) = 2γ(G), those for which γ(πG) = 2γ(G) for at least one permutation π of V(G) and those for which γ(πG) = 2γ(G) for each permutation π of V(G).
LA - eng
KW - domination; graph products; prisms of graphs
UR - http://eudml.org/doc/270590
ER -

## References

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1. [1] R. Bertolo, P.R.J. Ostergard and W.D. Weakley, An Updated Table of Binary/Ternary Mixed Covering Codes, J. Combin. Design, to appear. Zbl1054.94022
2. [2] N.L. Biggs, Algebraic Graph Theory, Second Edition (Cambridge University Press, Cambridge, England, 1996). Zbl0284.05101
3. [3] N.L. Biggs, Some odd graph theory, Ann. New York Acad. Sci. 319 (1979) 71-81, doi: 10.1111/j.1749-6632.1979.tb32775.x.
4. [4] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, New York, 1998). Zbl0890.05002
5. [5] S.M. Johnson, A new lower bound for coverings by rook domains, Utilitas Mathematica 1 (1972) 121-140. Zbl0265.05011
6. [6] O. Ore, Theory of Graphs, Amer. Math. Soc. Colloq. Publ. 38 (Amer. Math. Soc., Providence, RI, 1962).
7. [7] F.S. Roberts, Applied Combinatorics (Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1984).
8. [8] G.J.M. Van Wee, Improved Sphere Bounds On The Covering Radius Of Codes, IEEE Transactions on Information Theory 2 (1988) 237-245, doi: 10.1109/18.2632. Zbl0653.94014

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