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

Elvan Ceyhan ()
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Elvan Ceyhan: Koç University

Methodology and Computing in Applied Probability, 2012, vol. 14, issue 2, 299-334

Abstract: 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.

Keywords: Class cover catch digraph (CCCD); Class cover problem; Covering set; Delaunay triangulation; Minimum dominating set; Proportional-edge PCD; Proximity graph; Random graph; 60D05; 05C80; 05C20; 60C05 (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s11009-010-9204-9

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