| 双圈图的优美性 |
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| 引用本文： | 魏众德,李敬文,武永兰.双圈图的优美性[J].吉林大学学报(理学版),2019,57(1):42-48. |
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| 作者姓名： | 魏众德 李敬文 武永兰 |
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| 作者单位： | 兰州交通大学电子与信息工程学院,兰州,730070;兰州交通大学电子与信息工程学院,兰州,730070;兰州交通大学电子与信息工程学院,兰州,730070 |
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| 基金项目： | 国家自然科学基金;国家自然科学基金 |
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| 摘 要： | 针对双圈图, 设计一种图的优美性判定算法, 并对17个点内的所有双圈图进行优美性验证, 得到了该范围内所有的优美图和非优美图. 结果表明, 在17个顶点范围内, 除∞ 型双圈图C(m,n)外, 其余所有双圈图都是优美的, 其中(m+n)(mod 4)={1,2}. 最后给出该类图的非优美证明, 并进一步猜测当顶点数大于17时, 该结论仍成立.
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| 关 键 词： | 双圈图 优美图 优美标号 |
| 收稿时间： | 2017-12-28 |
Gracefulness of Bicyclic Graphs |
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| WEI Zhongde,LI Jingwen,WU Yonglan.Gracefulness of Bicyclic Graphs[J].Journal of Jilin University: Sci Ed,2019,57(1):42-48. |
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| Authors: | WEI Zhongde LI Jingwen WU Yonglan |
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| Institution: | School of Electronic and Information Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China
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| Abstract: | Aiming at the bicyclic graphs, we designed an algorithmto determine the gracefulness of graphs verified the gracefulness of all bicyclic graphs with at most 17 vertices, and obtained all graceful and ungraceful graphs in this range. The results show thatexcept ∞ shape bicyclic graphs C(m,n),all bicyclic graphs with at most 17 vertices are graceful, where (m+n)(mod 4)={1,2}. Finally, we gavea proof for the ungracefulness of this kind of graph, and further speculation that the conclusion still held true whenthe number of vertices was greater than 17. |
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| Keywords: | bicyclic graph graceful graph graceful labeling |
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