Title
Vertex-Edge Domination
Document Type
Article
Publication Date
3-1-2010
Description
Most of the research on domination focuses on vertices dominating other vertices. In this paper we consider vertexedge domination where a vertex dominates the edges incident to it as well as the edges adjacent to these incident edges. The minimum cardinality of a vertex-edge dominating set of a graph G is the vertex-edge domination number γve(G). We present bounds on γve(G) and relationships between γve(G) and other domination related parameters. Since any ordinary dominating set is also a vertex-edge dominating set, it follows that γve(G) is bounded above by the domination number of G. Our main result characterizes the trees having equal domination and vertex-edge domination numbers.
Citation Information
Lewis, Jason; Hedetniemi, Stephen T.; Haynes, Teresa W.; and Fricke, Gerd H.. 2010. Vertex-Edge Domination. Utilitas Mathematica. Vol.81 193-213. ISSN: 0315-3681