Some matching properties in 4-gamma(x2)-critical graphs
A vertex subset Sofa graph G = (V, E) is a double dominating set for G if |N[nu] boolean AND S| >= 2 for each vertex nu is an element of V. where |N[nu] = (u Iuv E E) U (v). The double domination number of G, denoted by gamma(x2)(G), is the cardinality of a smallest double dominating set of G. A graph G is said to be double domination edge critical if gamma(x2)(G+e)  = 6 except a family of graphs. Secondly, we show that G is bicritical if G is a 2-connected claw-free 4-y2(C)-critical graph of even order with minimum degree at least 3. Finally, we show that G is bicritical if G is a 3-connected K-1,K-4-free 4-gamma(x2)(C)-critical graph of even order with minimum degree at least 4. (C) 2009 Elsevier Ltd. All rights reserved.
matching bicritical claw-free double domination edge critical graphs