Domination critical graphs and matching properties.
by
Nawarat Ananchuen
Department of Mathematics, Faculty of Science, Silpakorn University, Nakorn Pathom, Thailand

A subset of vertices S of a graph G is a dominating set for G if every vertex of G not in S is adjacent to one in S. The cardinality of any smallest dominating set in G is denoted by g(G) and called the domination number of G. Graph G is said to be g-edge-critical if g(G+e) < g(G) for every edge e ∈ E([`G]) and G is said to be g-vertex-critical if g(G-v) < g(G) for every vertex v in G. In this talk, the results on matching properties in both g-edge-critical graphs and g-vertex-critical graphs are presented.

Date received: March 16, 2008