| 有向图n·■_m的优美性 |
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| 引用本文： | 包玉兰,冯伟,吉日木图.有向图n·■_m的优美性[J].数学的实践与认识,2008(24). |
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| 作者姓名： | 包玉兰 冯伟 吉日木图 |
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| 作者单位： | 内蒙古民族大学数学与计算机科学学院; |
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| 摘 要： | 给定有向图D(V,E),如果存在一个单射f:V(D)→{0,1,…,|E|}使得对于每条有向边(u,v),诱导函数f′:E(D)→{1,2,…,|E|}是一个双射函数,其中,f′(u,v)=f(v)-f(u)](mod(|E|+1)),则f称为有向图D(V,E)的优美标号,f′称为有向图D(V,E)的诱导的边的优美标号.本文讨论了有向图n.■m的优美性,并且证明了当m=23且n为偶数时,n.■m是优美有向图.
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| 关 键 词： | 有向图 有向圈 优美图 优美标号 |
On the Gracefulness of the Digraphs n·■_m |
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| BAO Yu-lan,FENG Wei,Jirimutu.On the Gracefulness of the Digraphs n·■_m[J].Mathematics in Practice and Theory,2008(24). |
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| Authors: | BAO Yu-lan FENG Wei Jirimutu |
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| Institution: | College of Mathematics and Computer;Inner Mongolian University for Nationalities;Tongliao 028043;China |
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| Abstract: | A digraph D(V,E) is said to be graceful if there exists an injection f:V(G)→{0,1,…,|E|} such that the induced function f′:E(G)→{1,2,…,|E|} which is defined by f′(u,v)={mod(|E|+1)) for every directed edge(u,v) is a bijection.Here,f is called a graceful labeling(graceful numbering) of D(V,E),and f′ is called the induced edge′s graceful labeling of D.In this paper we discuss the gracefulness of the digraph n·■m and prove that n·■m is a graceful digraph for m=23 and even n. |
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| Keywords: | digraph directed cycles graceful graph graceful labeling |
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