Some matching properties in 4-γ×2--critical graphs

Authors:
Haichao Wang;Erfang Shan
Affiliations:
Department of Mathematics, Shanghai University, Shanghai 200444, China and Department of Mathematics and Physics, Shanghai University of Electric Power, Shanghai 200090, China;Department of Mathematics, Shanghai University, Shanghai 200444, China
Venue:
Computers & Mathematics with Applications
Year:
2010

Citing 3
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Graph Theory With Applications

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Abstract

A vertex subset S of a graph G=(V,E) is a double dominating set for G if |N[v]@?S|=2 for each vertex v@?V, where N[v]={u|uv@?E}@?{v}. The double domination number of G, denoted by @c"x"2(G), is the cardinality of a smallest double dominating set of G. A graph G is said to be double domination edge critical if @c"x"2(G+e)=6 except a family of graphs. Secondly, we show that G is bicritical if G is a 2-connected claw-free 4-@c"x"2(G)-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","4-free 4-@c"x"2(G)-critical graph of even order with minimum degree at least 4.