| 拟无爪图的性质 |
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| 引用本文： | 王兵.拟无爪图的性质[J].山东大学学报(理学版),2007,42(10):111-113. |
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| 作者姓名： | 王兵 |
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| 作者单位： | 枣庄学院,数学系,山东,枣庄,277160 |
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| 基金项目： | 致谢：感谢刘桂真教授的悉心指导与热情鼓励. |
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| 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.
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| 关 键 词： | 拟无爪图 坚韧度 连通度 控制数 独立控制数 |
| 文章编号： | 1671-9352（2007）10-0111-03 |
| 修稿时间： | 2007-04-05 |
Properties of a quasi-claw-free graph |
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| WANG Bing.Properties of a quasi-claw-free graph[J].Journal of Shandong University,2007,42(10):111-113. |
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| Authors: | WANG Bing |
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| Institution: | Department of Mathematics, Shandong Zaozhuang College, Zaozhuang 277160, Shandong, China |
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| Abstract: | The properties of quasi-claw-free graphs were discussed, which are larger than claw-free graphs. and the following two results 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∈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 results in claw-free graph. |
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| Keywords: | quasi-claw-free graph toughness connectivity domination number independent domination number |
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