The Gracefulness of Unconnected Graphs (P3∨Km)∪G及(C3∨Km)∪G

WANG Tao; WANG Qing; LI Deming

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The Gracefulness of Unconnected Graphs (P₃∨K_m)∪G及(C₃∨K_m)∪G

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- The Gracefulness of Unconnected Graphs (P₃∨K_m)∪G及(C₃∨K_m)∪G
- Acta Scientiarum Naturalium Universitatis SunYatseni Vol. 51, Issue 5, Pages: 54-57(2012)
- 作者机构：
  
  1. 华北科技学院基础部,河北,三河,065201
  2. 首都师范大学数学系,北京,100048
- 作者简介：
- 基金信息：
- DOI：
  CLC：
- Published：2012，
  
  Published Online：25 September 2012，
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WANG Tao, WANG Qing, LI Deming. The Gracefulness of Unconnected Graphs (P₃∨K_m)∪G及(C₃∨K_m)∪G. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 51(5):54-57(2012)
DOI：

WANG Tao, WANG Qing, LI Deming. The Gracefulness of Unconnected Graphs (P₃∨K_m)∪G及(C₃∨K_m)∪G. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 51(5):54-57(2012) DOI：

摘要

将k--优美图的概念进行了推广，引入A～B优美图的概念，并以此为基础，得到了非连通图

是优美图的一个充分条件。证明了对任意正整数k

t，当k≤n≤t，n+k－1≤m时，图

j=1

) 和

j=1

)是优美图；当k=1

2，2≤n

2m+1时，图(P

∨K

)∪

∪

j=1

∨K

)∪

∪

j=1

n 和

∨K

)∪ P

∪St(t)是优美图；当2≤n≤2m+1时，(P

∨K

)∪ P

∪St(t) 是优美图。本文的结果推广了现有的一些结论。

Abstract

The definition of k－graceful graph is extended and the new concept of A～B graceful graph is presented．One sufficient condition about determining the gracefulness of unconnected graph

is obtained．In the meanwhile

it is proved that for any natural numbers

which are not less than one

when k≤n≤t and n+k－1≤m

the disconnected graphs

j=1

) and

j=1

) are graceful; when k=1

2≤n

2m+1 the graphs (P

∨K

)∪

∪

j=1

∨K

)∪

∪

j=1

and (P

∨K

)∪ P

∪St(t) are graceful; when 2≤n≤2m+1

the graphs (P

∨K

)∪ P

∪St(t) are graceful. Results generalize some of the known results.

关键词

图非连通图优美图优美标号

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The Gracefulness of Two Kinds of Unconnected Graphs#br# (P₂∨K_n)（0，0,r₁,0,…,0,r_n)∪St(m) and (P₂∨K_n)（r₁+a,r₂,0,…,0)∪G_r

Related Author

WU Yuesheng

XU Baogen

Related Institution

School of Basic Science, East China Jiaotong University

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