2类与4-圈有关图的优美性

吉林大学学报(理学版)

2类与4-圈有关图的优美性

唐保祥¹, 任韩²

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

收稿日期:2015-02-02 出版日期:2015-09-26 发布日期:2015-09-29
通讯作者: 唐保祥 E-mail:tbx0618@sina.com

Gracefulness of Two Types of Graphs Relatedto Cycles of Length Four

TANG Baoxiang¹, REN Han²

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

Received:2015-02-02 Online:2015-09-26 Published:2015-09-29
Contact: TANG Baoxiang E-mail:tbx0618@sina.com

摘要/Abstract

摘要：

把顺序有一个公共点的n个4圈的并图记作F_n,4; 图F_n,4每个4圈的顶点u_i1与u_i2之间连接m条长为2的路u_i1v_iju_i2(i,j=1,2,…,n)得到的图记为m-F_n,4; 将孤立顶点w与m-F_n,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-F_n,4+E_n(m+1). 用构造的方法给出图m-F_n,4和m-F_n,4+E_n(m+1)的优美标号, 并证明了m-F_n,4和m-F_n,4+E_n(m+1)都是优美图.

关键词: 4-圈, 优美图, 优美标号

Abstract:

The graph marked F_n,4 that is formed by n pieces of 4cycles with one common vertice in order. Let u_i1 and u_i2 be two vertices in graph F_n,4, which connect u_i1 and u_i2 with m paths of length 2 for u_i1v_iju_i2(i,j=1,2,…,n). The resulting graphs are denoted as m-F_n,4. Let G represent the graph obtained by connecting every vertex of graph m-F_n,4 isolated vertex w to an edge of it. Let m-F_n,4+E_n(m+1) be the graph obtained from G by attaching n(m+1) pendent edges to the vertex w of graph G. The constructor method gives graceful labeling of m-F_n,4and m-F_n,4+E_n(m+1), thus proving graceful graphs m-F_n,4 and m-F_n,4+E_n(m+1). Thus, a series of graceful graphs can be constructed from one graceful graph.

Key words: 4-cycles, graceful graph, graceful labeling

中图分类号:

O157.5

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(05): 893-896.

TANG Baoxiang, REN Han. Gracefulness of Two Types of Graphs Relatedto Cycles of Length Four[J]. Journal of Jilin University Science Edition, 2015, 53(05): 893-896.

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