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  Research Program **

Week 2 Topic
Concepts of Domination in Graphs and Directed Graphs
July 26 - 30, 1999

Chair: K. Brooks Reid, California State University breid@mailhost1.csusm.edu



Speakers & Participants


A dominating set in a graph G (or a digraph D) with vertex set V is a subset S of V with the property that for every vertex x in V - S there is some vertex s in S so that {s, x} is an edge of G (respectively, (s, x) is a directed edge of D}. The minimum cardinality of a dominating set in G (or D) is called the domination number of G (respectively, D). This natural graphical parameter has been well studied, and it continues to provide researchers with a host of interesting, and often applicable, problems and issues. Conditions on the set S or on V - S or on some other part of the definition have provided for many new and intriguing avenues of pursuit for researchers in the area. This conference will bring together many of the active researchers in this area to discuss their work and its applications. Topics in digraphs may include work on domination numbers, Schütte's problems for tournaments, transitivity, reachability, kernels, kings, domination and competition graphs, and applications. Topics in undirected graphs may include work on domination, independence and irredundance numbers and their variants and generalizations, and applications. Effort will be made to include some topics and activities that have the potential for inclusion in high school mathematics classrooms.