| 顾彦波, 李敬文, 火金萍, 邵淑宏.图(p≤9)的边幻和全标号[J].,2020,60(4):427-436 |
| 图(p≤9)的边幻和全标号 |
| Edge-magic total labeling of graphs(p≤9) |
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| DOI：10.7511/dllgxb202004012 |
| 中文关键词: 递归算法 边幻和全标号 非边幻和全标号 边幻和全标号解空间 |
| 英文关键词: recursive algorithm edge-magic total labeling non-edge-magic total labeling edge-magic total labeling solution space |
| 基金项目:国家自然科学基金资助项目(11461038). |
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| 中文摘要: |
| 图的边幻和全标号是指图中任意边及其两个顶点的标号和为常数,且标号取值一一对应于从1至点边之和的自然数集合.设计了一种递归算法,采用了与目标函数相结合的算法优化策略,实现了对9个点内所有简单连通图的边幻和性判定.结果表明,当p≤9时,所有的树图、单圈图和双圈图都是边幻和全标号图;当点边数值满足一定条件时,发现若干图类是边幻和全标号图或非边幻和全标号图,结合已有结果,猜测当点数超过9时,相关结论也成立.其中,已经证明点数不超过12时的猜测成立. |
| 英文摘要: |
| The edge-magic total labeling of a graph means that the labeling sum of any edge and its two vertices in a graph is a constant, and the labeling values fully correspond to the set of natural number from 1 to the sum of the vertices and edges. A recursive algorithm is designed, which combines the algorithm optimization strategy with the objective function to realize the edge-magic judgment of all simple connected graphs in 9 vertices. The results show that when p≤9, all the tree graphs, unicyclic graphs and bicyclic graphs are edge-magic total labeling graphs. When the labeling values of vertex and edge satisfy certain conditions, it is found that several graph classes are edge-magic total labeling graphs or non-edge-magic total labeling graphs. Combining the existing results, it can be conjectured that when the number of vertices exceeds 9, the relevant conclusions are also valid. Among them, it has been proven that the conjecture is valid when the number of vertices is no more than 12. |
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