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An Investigation of New Graph Invariants Related to the Domination Number of Random Proximity Catch Digraphs

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  • Elvan Ceyhan

    (Koç University)

Abstract

Proximity catch digraphs (PCDs) are a special type of proximity graphs based on proximity maps which yield proximity regions. PCDs are defined using the relative allocation of points from two or more classes in a region of interest and have applications in various fields. We introduce some auxiliary tools for PCDs and graph invariants related to the domination number of the PCDs and investigate their probabilistic properties. We consider the cases in which the vertices of the PCDs come from uniform and non-uniform distributions in the region of interest. We also provide some of the newly defined proximity maps as illustrative examples.

Suggested Citation

  • Elvan Ceyhan, 2012. "An Investigation of New Graph Invariants Related to the Domination Number of Random Proximity Catch Digraphs," Methodology and Computing in Applied Probability, Springer, vol. 14(2), pages 299-334, June.
    • Handle: RePEc:spr:metcap:v:14:y:2012:i:2:d:10.1007_s11009-010-9204-9
    DOI: 10.1007/s11009-010-9204-9
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    References listed on IDEAS

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    1. Ceyhan, Elvan & Priebe, Carey E., 2005. "The use of domination number of a random proximity catch digraph for testing spatial patterns of segregation and association," Statistics & Probability Letters, Elsevier, vol. 73(1), pages 37-50, June.
    2. Priebe, Carey E. & DeVinney, Jason G. & Marchette, David J., 2001. "On the distribution of the domination number for random class cover catch digraphs," Statistics & Probability Letters, Elsevier, vol. 55(3), pages 239-246, December.
    3. Wierman, John C. & Xiang, Pengfei, 2008. "A general SLLN for the one-dimensional class cover problem," Statistics & Probability Letters, Elsevier, vol. 78(9), pages 1110-1118, July.
    4. Xiang, Pengfei & Wierman, John C., 2009. "A CLT for a one-dimensional class cover problem," Statistics & Probability Letters, Elsevier, vol. 79(2), pages 223-233, January.
    5. Ceyhan, Elvan & Priebe, Carey E. & Wierman, John C., 2006. "Relative density of the random r-factor proximity catch digraph for testing spatial patterns of segregation and association," Computational Statistics & Data Analysis, Elsevier, vol. 50(8), pages 1925-1964, April.
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