Discussiones Mathematicae Graph Theory 32(2) (2012)
299-319

doi: 10.7151/dmgt.1600

Linda Eroh, Ralucca Gera^{1}, Cong X. Kang^{2} ,^{3}Craig E. Larson and Eunjeong Yi^{4}^{3}
University of Wisconsin Oshkosh Oshkosh, WI 54901, USA Department of Applied Mathematics^{2}Naval Postgraduate School |

**Keywords:** domination, permutation graphs, generalized prisms, functigraphs

**2010 Mathematics Subject Classification:** 05C69, 05C38.

[1] | S. Benecke, Domination of generalized Cartesian products, Ph.D. Dissertation (University of Victoria, 2009). |

[2] | S. Benecke and C.M. Mynhardt, Domination of generalized Cartesian products, Discrete Math. 310 (2010) 1392--1397, doi: 10.1016/j.disc.2009.12.007. |

[3] | C. Berge, Graphs and Hypergraphs (North-Holland, Amsterdam,1973). |

[4] | C. Berge, Theory of Graphs and its Applications (Methuen, London, 1962). |

[5] | A.P. Burger and C.M. Mynhardt, Regular graphs are not universal fixers, Discrete Math. 310 (2010) 364--368, doi: 10.1016/j.disc.2008.09.016 . |

[6] | 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. |

[7] | G. Chartrand and F. Harary, Planar permutation graphs, Ann. Inst. H. Poincare (Sect. B) 3 (1967) 433--438. |

[8] | G. Chartrand and P. Zhang, Introduction to Graph Theory (McGraw-Hill, Kalamazoo, MI, 2004). |

[9] | A. Chen, D. Ferrero, R. Gera and E. Yi, Functigraphs: An Extension of Permutation Graphs, Math. Bohem. 136 (2011) 27--37. |

[10] | E.J. Cockayne and S.T. Hedetniemi, Towards a theory of domination in graphs, Networks 7 (1977) 247--261, doi: 10.1002/net.3230070305. |

[11] | W. Dörfler, On mapping graphs and permutation graphs, Math. Slovaca 28 (1978) 277--288. |

[12] | B.L. Hartnell and D.F. Rall, On dominating the cartesian product of a graph and , Discuss. Math. Graph Theory K_{2}24 (2004) 389--402, doi: 10.7151/dmgt.1238. |

[13] | T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Domination in Graphs: Advanced Topics (Marcel Dekker, New York, 1998). |

[14] | T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, New York, 1998). |

[15] | S.T. Hedetniemi, On classes of graphs defined by special cutsets of lines, Many Facets of Graph Theory, Lect. Notes Math. 110 (1969) 171--189, doi: 10.1007/BFb0060115. |

[16] | O. Ore, Theory of Graphs (Amer. Math. Soc. Colloq. Publ., 38, Providence, 1962). |

Received 12 July 2010

Revised 6 June 2011

Accepted 6 June 2011