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2007 | 27 | 1 | 51-67
Tytuł artykułu

Digraphs with isomorphic underlying and domination graphs: connected $UG^c(d)$

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The domination graph of a directed graph has an edge between vertices x and y provided either (x,z) or (y,z) is an arc for every vertex z distinct from x and y. We consider directed graphs D for which the domination graph of D is isomorphic to the underlying graph of D. We demonstrate that the complement of the underlying graph must have k connected components isomorphic to complete graphs, paths, or cycles. A complete characterization of directed graphs where k = 1 is presented.
Wydawca
Rocznik
Tom
27
Numer
1
Strony
51-67
Opis fizyczny
Daty
wydano
2007
otrzymano
2005-09-21
poprawiono
2006-06-24
Twórcy
  • Marquette University, P.O. Box 1881, Milwaukee, WI 53201-1881, USA
  • University of the Pacific, 3601 Pacific Avenue Stockton, CA 95211, USA
Bibliografia
  • [1] B.D. Acharya and M.N. Vartak, Open neighbourhood graphs, Indian Institute of Technology Dept. of Mathematics Research Report No. 7, Bombay-400 076, India (1973).
  • [2] D.B. Bergstrand and L. Friedler, Domination graphs of tournaments and other digraphs, Ars Combinatoria 74 (2005) 89-96.
  • [3] R.C. Brigham and R.D. Dutton, On neighbourhood graphs, J. Combin., Information & System Sciences 12 (1987) 75-85.
  • [4] H.H. Cho, S.R. Kim and J.R. Lundgren, Domination graphs of regular tournaments, Discrete Math. 252 (2002) 57-71, doi: 10.1016/S0012-365X(01)00289-8.
  • [5] H.H. Cho, F. Doherty, S.R. Kim and J.R. Lundgren, Domination graphs of regular tournaments II, Congress. Numer. 130 (1998) 95-111.
  • [6] C. Cocking and K.A.S. Factor, Domination-stable forms of complete biorientations of some classes of graphs, Congress. Numer. 160 (2003) 83-96.
  • [7] G. Exoo and F. Harary, Step graphs, J. Combin. Information & System Sciences 5 (1987) 52-53.
  • [8] J.D. Factor and K.A.S. Factor, Partial domination graphs of extended tournaments, Congress. Numer. 158 (2002) 119-130.
  • [9] K.A.S. Factor and L.J. Langley, Characterization of Digraphs with Equal Domination Graphs and Underlying Graphs, preprint (2005).
  • [10] K.A.S. Factor, Domination graphs of compressed tournaments, Congress. Numer. 157 (2002) 63-78.
  • [11] D.C. Fisher, D. Guichard, S.K. Merz and J.R. Lundgren, Domination graphs with nontrivial components, Graphs and Combin. 17 (2001) 227-228, doi: 10.1007/s003730170036.
  • [12] D.C. Fisher, D. Guichard, J.R. Lundgren, S.K. Merz and K.B. Reid, Domination graphs with 2 or 3 nontrivial components, Bulletin of the ICA 40 (2004) 67-76.
  • [13] D.C. Fisher, D. Guichard, J.R. Lundgren, S.K. Merz and K.B. Reid, Domination graphs of tournaments with isolated vertices, Ars Combin. 66 (2003) 299-311.
  • [14] D.C. Fisher, J.R. Lundgren, S.K. Merz and K.B. Reid, Connected domination graphs of tournaments, JCMCC 31 (1999) 169-176.
  • [15] D.C. Fisher, J.R. Lundgren, S.K. Merz and K.B. Reid, The domination and competition graphs of a tournament, J. Graph Theory 29 (1998) 103-110, doi: 10.1002/(SICI)1097-0118(199810)29:2<103::AID-JGT6>3.0.CO;2-V
  • [16] D.C. Fisher, J.R. Lundgren, S.K. Merz and K.B. Reid, Domination graphs of tournaments and digraphs, Congress. Numer. 108 (1995) 97-107.
  • [17] H.J. Greenburg, J.R. Lundgren and J.S. Maybee, The inversion of 2-step graphs, J. Combin. Information & System Sciences 8 (1983) 33-43.
  • [18] J.R. Lundgren, J.S. Maybee and C.W. Rasmussen, Interval competition graphs of symmetric digraphs, Discrete Math. 119 (1993) 113-123, doi: 10.1016/0012-365X(93)90121-9.
  • [19] J.R. Lundgren, J.S. Maybee and C.W. Rasmussen, An application of generalized competition graphs to the channel assignment problem, Congress. Numer. 71 (1990) 217-224.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1344
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