| 三路树P(2m,2m,2m)是边幻图的证明 |
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| 引用本文： | 路永洁.三路树P(2m,2m,2m)是边幻图的证明[J].洛阳师范学院学报,2000,19(5):19-20. |
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| 作者姓名： | 路永洁 |
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| 作者单位： | 抚顺石油学院数理部,辽宁,抚顺,11300 |
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| 摘 要： | 令简单图G =(V ,E)是有p个顶点q条边的图 .假设G的顶点和边由 1 ,2 ,3,… ,p +q所标号 ,且f:V∪E {1 ,2 ,… ,p+q}是一个双射 .如果对所有的边xy ,f(x) +f(y)+f(xy)是常量 ,则称图G是边幻图 (edge magic) .文 1 ]中猜测树是边幻图 .本文证明了三路树P(m ,n ,t)当m ,n ,t为偶数且相等时为边幻图 .
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| 关 键 词： | 三路树 边幻图 |
| 文章编号： | 1009-4970(2000)05-0019-02 |
| 修稿时间： | 2000年1月4日 |
Proof of Three-path P(2m, 2m, 2m)Being Edge-magic Graph |
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| LU Yong,jie.Proof of Three-path P(2m, 2m, 2m)Being Edge-magic Graph[J].Journal of Luoyang Teachers College,2000,19(5):19-20. |
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| Authors: | LU Yong jie |
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| Abstract: | Let G be a graph with p vertices and q edges. Assume the vertices and edges of G are labelled by 1, 2, 3…, p+q such that each label is used exactly once. We define the valence vale of an edge to be the sum of the label of e plus the two labels pf the vertices incident with e. If a labelling of G is possible such that the valence vale for e is constant, we call the graph G is edge magic. Reference1]proposed the conjecture: every tree is edge magic. In this paper, we prove that P(2m, 2m, 2m)is edge magic. |
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| Keywords: | tree three -path edge-magph graph |
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