
Properties of a quasiclawfree graph
 WANG Bing

J4. 2007, 42(10):
111113 .
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The properties of quasiclawfree graphs were discussed, which are larger than clawfree graphs. and the following two results were obtained: if G is a quasiclawfree graph, then (ⅰ) 2t(G)=κ(G), where ω(GS)≤t(G).(ⅱ) For every dominating set D and each t∈D, there are at most three vetices u1,u2,u3∈(VD) satisfying, N(ui)∩D={t}(i=1,2,3), then γ(G)=i(G). This result is the best possible. These results extend the corresponding results in clawfree graph.