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Domination Graphs with Nontrivial Components

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Abstract.

 A tournament is an oriented complete graph. Vertices x and y dominate a tournament T if for all vertices z≠x,y, either (x,z) or (y,z) are arcs in T (possibly both). The domination graph of a tournament T is the graph on the vertex set of T containing edge {x,y} if and only if x and y dominate T. In this paper we determine which graphs containing no isolated vertices are domination graphs of tournaments.

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Authors and Affiliations

  1.  The University of Colorado at Denver, Denver, CO 80217-3364, USA, , , , , , US

    David C. Fisher & J. Richard Lundgren

  2.  Whitman College, Walla Walla, WA 99362, USA, , , , , , US

    David Guichard

  3.  Department of Mathematics, The University of the Pacific, Stockton, CA 95211, USA e-mail: smerz@uop.edu, , , , , , US

    Sarah K. Merz

  4.  California State University, San Marcos, CA 92096-0001, USA, , , , , , US

    K. Brooks Reid

Authors
  1. David C. Fisher
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  2. David Guichard
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  3. J. Richard Lundgren
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  4. Sarah K. Merz
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  5. K. Brooks Reid
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Received: May 20, 1998 Final version received: May 26, 1999

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Fisher, D., Guichard, D., Lundgren, J. et al. Domination Graphs with Nontrivial Components. Graphs Comb 17, 227–236 (2001). https://doi.org/10.1007/s003730170036

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  • DOI: https://doi.org/10.1007/s003730170036

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