| 2类与4-圈有关图的优美性 |
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| 引用本文： | 唐保祥,任韩. 2类与4-圈有关图的优美性[J]. 吉林大学学报(理学版), 2015, 53(5): 893-896 |
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| 作者姓名： | 唐保祥 任韩 |
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| 作者单位： | 1. 天水师范学院 数学与统计学院, 甘肃 天水 741001; 2. 华东师范大学 数学系, 上海 200062 |
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| 摘 要： | 把顺序有一个公共点的n个4圈的并图记作Fn,4;图Fn,4每个4圈的顶点ui1与ui2之间连接m条长为2的路ui1vijui2(i,j=1,2,…,n)得到的图记为m-Fn,4;将孤立顶点w与m-Fn,4的每个顶点连接一条边得到的图记为G,将图G的顶点w加n(m+1)条悬挂边所得到的图记为m-Fn,4+En(m+1).用构造的方法给出图m-Fn,4和m-Fn,4+En(m+1)的优美标号,并证明了m-Fn,4和m-Fn,4+En(m+1)都是优美图.
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| 关 键 词： | 4-圈 优美图 优美标号 |
| 收稿时间： | 2015-02-02 |
Gracefulness of Two Types of Graphs Related to Cycles of Length Four |
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| TANG Baoxiang,REN Han. Gracefulness of Two Types of Graphs Related to Cycles of Length Four[J]. Journal of Jilin University: Sci Ed, 2015, 53(5): 893-896 |
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| Authors: | TANG Baoxiang REN Han |
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| Affiliation: | 1. School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001, Gansu Province, China;2. Department of Mathematics, East China Normal University, Shanghai 200062, China |
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| Abstract: | The graph marked Fn,4 that is formed by n pieces of 4 cycles with one common vertice in order. Let ui1 and ui2 be two vertices in graph Fn,4, which connect ui1 and ui2 with m paths of length 2 for ui1vijui2(i,j=1,2,…,n). The resulting graphs are denoted as m-Fn,4. Let G represent the graph obtained by connecting every vertex of graph m-Fn,4 isolated vertex w to an edge of it. Let m-Fn,4+En(m+1) be the graph obtained from G by attaching n(m+1) pendent edges to thevertex w of graph G. The constructor method gives graceful labeling of m-Fn,4 and m-Fn,4+En(m+1), thus proving graceful graphs m-Fn,4 and m-Fn,4+En(m+1). Thus, a series of graceful graphs can be constructed from one graceful graph. |
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| Keywords: | 4-cycles graceful graph graceful labeling |
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