Planar domination graphs

Authors:
Elaine M. Eschen;William F. Klostermeyer;R. Sritharan
Affiliations:
Lane Department of Computer Science and Electrical Engineering, West Virginia University, P.O. Box 6109, Morgantown, WV;Computer and Information Sciences, University of North Florida, Jacksonville, FL;Computer Science Department, The University of Dayton, Dayton, OH
Venue:
Discrete Mathematics
Year:
2003

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Abstract

A graph G is a domination graph if each induced subgraph of G has a pair of vertices such that the open neighborhood of one is contained in the closed neighborhood of the other in the subgraph. No polynomial time algorithm or hardness result is known for the problem of deciding whether a graph is a domination graph. In this paper, it is shown that the class of planar domination graphs is equivalent to the class of planar weakly chordal graphs, and thus, can be recognized in polynomial time.