两类非连通图优美性的研究

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两类非连通图优美性的研究

魏丽侠, 闫守峰, 张昆龙

华北科技学院基础部, 河北三河 065200

收稿日期:1900-01-01 修回日期:1900-01-01 出版日期:2006-10-24 发布日期:2006-10-24
通讯作者: 魏丽侠

The researches on gracefilness of two kinds of unconnected graphs

WEI Li-xia, YAN Shou-feng, ZHANG Kun-long

Department of Basic Courses North China Institute of Science and Technology, Sanhe 065200, Hebei, China

Received:1900-01-01 Revised:1900-01-01 Online:2006-10-24 Published:2006-10-24
Contact: WEI Li-xia

摘要/Abstract

摘要：

给出了两类非连通图(K2〖TX-〗∨Cn)∪[DD(]3[]i=1[DD)]St(mi)和
(K2〖TX-〗∨C2n+k)∪St(m)∪G(k)n-1(k=1,2), 并证明了如下结论:对自然数n, m, m1, m2, m3, 设s=〖JB(［〗〖SX(〗n〖〗2〖SX)〗〖JB)］〗, n≥9, m1≥s+2, 则图(K2〖TX-〗∨Cn)∪[DD(]3[]i=1[DD)]St(mi)是一个优美图; 对 k=1,2,设n, m≥3, G(k)n-1是一个具有n-1条边的k-优美图,则图(K2〖TX-〗∨C2n+k)∪St(m)∪G(k)n-1是一个优美图。其中,K2是一个具有2个顶点的完全图,K2〖TX-〗是图K2的补图,K2〖TX-〗∨Cn是图K2和n圈Cn的联图, St(m)是一个具有m+1个顶点的星形树。

关键词: 优美图, 星形树, 非连通图, 优美标号

Abstract:

Two kinds of unconnected graphs (K2〖TX-〗∨Cn)∪[DD(]3[]i=1[DD)]St(mi) and (K2〖TX-〗∨C2n+k)∪St(m)∪G(k)n-1(k=1,2) were presented, and following results were proved: for natural number n, m, m1, m2, m3, let s=〖JB(［〗〖SX(〗n〖〗2〖SX)〗〖JB)］〗, n≥9, m1≥s+2, then graph (K2〖TX-〗∨Cn)∪[DD(]3[]i=1[DD)]St(mi) is a graceful graph; for k=1,2, let n, m≥3, and let G(k)n-1 be a k-graceful graph with n-1 edges, then graph (K2〖TX-〗∨C2n+k)∪St(m)∪G(k)n-1 is a graceful graph. Where K2 bea complete graph with 2 vertices, K2〖TX-〗 is the complement of graph K2, graph K2〖TX-〗∨Cn is the join graph of K2〖TX-〗 and n-cycle Cn, St(m) isa star tree with m+1 vertices.

Key words: star tree, unconnected graph, graceful label, graceful graph

中图分类号:

O157.9

魏丽侠,闫守峰,张昆龙 .

两类非连通图优美性的研究

[J]. J4, 2008, 43(8): 90-96 .

WEI Li-xia,YAN Shou-feng,ZHANG Kun-long . The researches on gracefilness of two kinds of unconnected graphs[J]. J4, 2008, 43(8): 90-96 .

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