全变换图G^xyz  

Total Transformation Graphs G^xyz

作　　者：李亚平 吴宝音都仍 LI Yaping;WU Baoyindureng(School of Mathematics and System Sciences,Xinjiang University,Urumqi Xinjiang 830046,China)

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830046

出　　处：《新疆大学学报（自然科学版）（中英文）》2021年第1期1-24,共24页Journal of Xinjiang University(Natural Science Edition in Chinese and English)

基　　金：国家自然科学基金项目(11571294)。

摘　　要：设G=(V (G),E(G))是一个简单无向图, x,y,z是取+或-的3个变量.图G的变换图G^xyz是以V (G)∪E(G)为其顶点集,且对任意的α,β∈V (G)∪E(G),α,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G^xyz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G^xyz的已知结论与未解决的问题进行综述.Let G=(V(G),E(G))be a simple undirected graph of order n and size m,and x,y,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 vertexαandβare joined by an edge if one of the following conditions holds:(i)forα,β∈V(G),andαβ∈E(G)if x=+,andαβE(G)if x=-,(ii)forα,β∈E(G),andαandβare adjacent in G if y=+,andαandβare not adjacent in G if y=-,(iii)one ofαandβis in V(G)and the other is in E(G),and they are incident in G if z=+,andαandβare not incident in G if z=-.The transformation graph G^xyz 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 G^xyz.

关 键 词：全图 全变换图 补图 图参数 

分 类 号：O157.5[理学—基础数学]