The Gracefulness of Unconnected Graphs  (K1∨(P(1)n∪ P(2)n)) ∪ P(3)n  and  (K1∨(P(1)n∪ P(2)n)) ∪ P(3)n∪ St(n)

SUN Caiyun; WANG Tao

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The Gracefulness of Unconnected Graphs (K₁∨(P⁽¹⁾_n∪ P⁽²⁾_n)) ∪ P⁽³⁾_nand (K₁∨(P⁽¹⁾_n∪ P⁽²⁾_n)) ∪ P⁽³⁾_n∪ St(n)

更新时间：2023-12-11

- The Gracefulness of Unconnected Graphs (K₁∨(P⁽¹⁾_n∪ P⁽²⁾_n)) ∪ P⁽³⁾_nand (K₁∨(P⁽¹⁾_n∪ P⁽²⁾_n)) ∪ P⁽³⁾_n∪ St(n)
- Acta Scientiarum Naturalium Universitatis SunYatseni Vol. 53, Issue 3, Pages: 52-56(2014)
- 作者机构：
  
  华北科技学院,河北,三河,065201
- 作者简介：
- 基金信息：
- DOI：
  CLC：
- Published：2014，
  
  Published Online：25 May 2014，
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SUN Caiyun, WANG Tao. The Gracefulness of Unconnected Graphs (K₁∨(P⁽¹⁾_n∪ P⁽²⁾_n)) ∪ P⁽³⁾_nand (K₁∨(P⁽¹⁾_n∪ P⁽²⁾_n)) ∪ P⁽³⁾_n∪ St(n). [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 53(3):52-56(2014)
DOI：

SUN Caiyun, WANG Tao. The Gracefulness of Unconnected Graphs (K₁∨(P⁽¹⁾_n∪ P⁽²⁾_n)) ∪ P⁽³⁾_nand (K₁∨(P⁽¹⁾_n∪ P⁽²⁾_n)) ∪ P⁽³⁾_n∪ St(n). [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 53(3):52-56(2014) DOI：

摘要

给出了非连通图(K

∨(P

(1)

∪ P

(2)

)) ∪ P

(3)

和(K

∨(P

(1)

∪ P

(2)

)) ∪ P

(3)

∪ St(n)，且对其优美性进行了研究。证明了如下结论：设 n 为任意正整数，则当n≥4时，非连通图 (K

∨(P

(1)

∪ P

(2)

)) ∪ P

(3)

和(K

∨(P

(1)

∪ P

(2)

)) ∪ P

(3)

∪ St(n)均是优美图；其中，Pn 是 n 个顶点的路，Kn 是n个顶点的完全图， St(n) 是 n+1 个顶点的星形树，G

∨ G

是图 G1 与 G2 的联图。

Abstract

The unconnected graphs (K

∨(P

(1)

∪ P

(2)

)) ∪ P

(3)

and (K

∨(P

(1)

∪ P

(2)

)) ∪ P

(3)

∪ St(n) are presented，and their gracefulness is studied.It is proved that for positive integer n，if n≥4 then the unconnected graphs  (K

∨(P

(1)

∪ P

(2)

)) ∪ P

(3)

and (K

∨(P

(1)

∪ P

(2)

)) ∪ P

(3)

∪ St(n) are graceful graphs；if n≥3 and m≥s then unconnected graph W

∪ St(m) is a graceful graph；in the meanwhile．Where P

is n vertex path，K

is n vertex complete graph，St(n) is (n+1) vertex star tree

graph G

∨G

is the join graph of G1 and G2． 

关键词

优美图优美标号非连通图

Keywords

graceful graphgraceful labelunconnected graph

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