Discussiones Mathematicae Graph Theory 33(2) (2013) 437-456
doi: 10.7151/dmgt.1681

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Edge Dominating Sets and Vertex Covers

Ronald Dutton

Department of Computer Science
University of Central Florida,
Orlando, FL, USA

William F. Klostermeyer

School of Computing
University of North Florida
Jacksonville, FL 32224-26 USA

Abstract

Bipartite graphs with equal edge domination number and maximum matching cardinality are characterized. These two parameters are used to develop bounds on the vertex cover and total vertex cover numbers of graphs and a resulting chain of vertex covering, edge domination, and matching parameters is explored. In addition, the total vertex cover number is compared to the total domination number of trees and grid graphs.

Keywords: edge dominating set, matching, total dominating set, vertex cover

2010 Mathematics Subject Classification: 05C69, 05C70.

References

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Received 5 January 2012
Revised 26 June 2012
Accepted 26 June 2012