拟无爪图的性质  

Properties of a quasi-claw-free graph

作　　者：王兵[1] 

机构地区：[1]枣庄学院数学系,山东枣庄277160

出　　处：《山东大学学报（理学版）》2007年第10期111-113,共3页Journal of Shandong University(Natural Science)

摘　　要：讨论了比无爪图更广泛的图——拟无爪图,得到了以下两个结果:(ⅰ)若图G是拟无爪图,且满足ω(G-S)≤t(G),则2t(G)=κ(G).(ⅱ)若图G是拟无爪图,对于任意的控制集D及任意t∈D,至多存在3点u1,u2,u3∈(V-D)满足N(ui)∩D={t}(i=1,2,3),则γ(G)=i(G),该结果是最好可能的.以上结果扩展了无爪图的相应结果.The properties of quasi-claw-free graphs were discussed, which are larger than claw-free graphs. The following two resuhs were obtained： if G is a quasi-claw-free graph, then （ i ） 2t（G）=κ（G）, where ω（G-S）≤t（G） （ ii ） For every dominating set D and each t E D, there are at most three vetices u1, u2, u3 ∈ （ V - D） 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 resuhs in a claw-free graph.

关 键 词：拟无爪图 坚韧度 连通度 控制数 独立控制数 

分 类 号：O157[理学—数学]