全变换图G<sup>xyz</sup>

李亚平; 吴宝音都仍

doi:10.13568/j.cnki.651094.651316.2020.03.22.0001

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全变换图G^xyz

数理科学 | 更新时间：2026-01-21

- 全变换图G^xyz
- 全变换图G^xyz
- 新疆大学学报（自然科学版中英文） 2021年38卷第1期页码：1-24
- 作者机构：
  
  新疆大学数学与系统科学学院
- 作者简介：
- 基金信息：
  
  国家自然科学基金项目（11571294）~~
- DOI：10.13568/j.cnki.651094.651316.2020.03.22.0001
  中图分类号： O157.5
- 纸质出版：2021
- 稿件说明：
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[1]李亚平,吴宝音都仍.全变换图G~(xyz)[J].新疆大学学报(自然科学版)(中英文),2021,38(01):1-24.
[1]李亚平,吴宝音都仍.全变换图G~(xyz)[J].新疆大学学报(自然科学版)(中英文),2021,38(01):1-24. DOI： 10.13568/j.cnki.651094.651316.2020.03.22.0001.

DOI：10.13568/j.cnki.651094.651316.2020.03.22.0001.

摘要

设G=(V (G)

E(G))是一个简单无向图

z是取+或-的3个变量.图G的变换图Gxyz是以V (G)∪E(G)为其顶点集

且对任意的α

β∈V (G)∪E(G)

β相邻当且仅当以下条件之一成立:(i)α

β∈V (G)

x=+时当且仅当α和β在图G中相邻

x=-时当且仅当α和β在图G中不相邻;(ii)α

β∈E(G)

y=+时当且仅当α和β在图G中相邻

y=-时当且仅当α和β在图G中不相邻;(iii)α∈v(G)

β∈E(G)

z=+时当且仅当α和β在图G中关联

z=-时当且仅当α和β在图G中不关联.变换图Gxyz作为全图的变形是由吴和孟在2001年首次提出的.自那时起

大量的工作致力于研究这些变换图的各种性质.本文主要是对变换图Gxyz的已知结论与未解决的问题进行综述.

Abstract

Let G =(V(G)

E(G)) be a simple undirected graph of order n and size m

and x

z be three variables taking value+ or-. The transformation graph Gxyz of G is the graph with vertex set V(G) ∪ E(G) in which the vertex α and β are joined by an edge if one of the following conditions holds:(i) for α

β ∈ V(G)

and αβ ∈ E(G) if x = +

and αβ E(G) if x =-

(ii) forα

β ∈ E(G)

and α and β are adjacent in G if y = +

and α and β are not adjacent in G if y =-

(iii) one of α and β is in V(G) and the other is in E(G)

and they are incident in G if z = +

and α and β are not incident in G if z =-. The transformation graph Gxyz was first introduced by Wu and Meng in 2001

as the variation of the total graph. Since then

a large number of works are devoted to investigate various kinds of properties of these transformation graphs. In this paper

we summerize the results and unsolved problems on Gxyz .

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references

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全图的圈连通度(英文)

G^---的平面性(英文)

关于全图补图的完美匹配(英文)

全变换图Gxyz

全变换图Gxyz

DOI：10.13568/j.cnki.651094.651316.2020.03.22.0001

摘要

Abstract

关键词

Keywords

references

全变换图G^xyz

全变换图G^xyz