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

您当前的位置：

首页 >

文章列表页 >

全变换图G^xyz

更新时间：2026-01-21

- 全变换图G^xyz
- Journal of Xinjiang University (Natural Science Edition in Chinese and English) Vol. 38, Issue 1, Pages: 1-24(2021)
- 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：
- DOI：10.13568/j.cnki.651094.651316.2020.03.22.0001
  CLC： O157.5
- Published：2021
- 稿件说明：
移动端阅览
[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 .

关键词

Keywords

references

WU B Y D R,MENG J X.Basic properties of total transformation graphs[J].J Math Study,2001,34:109-116.

BONDY J A,MURTY U S R.Graph Theory with Applications[M].New York:The Macmillan Press,1976.

LIN Q,SHU J L.Regularity and spectral radius of transformation graphs[J].OR Transactions,2007,11:102-110.

KURATOWSKI C.Sur le probl`eme des courbes gauches en topolgie[J].Fund Math,1930,15:271-283.

BEHZAD M.A criterion for the planarity of the total graph of a graph[J].Proc Cambridge Philos Soc,1967,63:679-681.

YUAN L,LIU X P.On the planarity of G++-[J].American J Appl Math,2018,6:23-27.

WANG D,LIU X P.The planarity of G+--[J].Advances in Appl Math,2018,7:237-242.

WU B Y D R,ZHANG L,ZHANG Z.The transformation graph Gxyzwhen xyz=-++[J].Discrete Math,2005,296:263-270.

WANG L.On the planarity of some transformation graphs[J].Journal of Huaihua University,2007,26,8.

LIU X P.On the planarity of G---[J].Journal of Xinjiang University(Natural Science Edition),2006,23(2):159-161.

GR¨UNBAUM B.Incidence patterns of graphs and complexes,in The many Facets of Graph Theory,Letcure Notes in Mathematics110 (ed.G.Chartrand and S.F.Kapoor)[C].New York:Springer-Verlag Berlin Heiderlberg,1969,115-128.

CHV′ATAL V,ERD?OS P.A note on Hamiltonian circuits[J].Discrete Math,1972,2:111-113.

FLEISCHNER H.On spanning subgraphs of a connected bridgeless graph and their application to DT-graphs[J].J Combinatorial Theory Ser B,1974,16(1):17-28.

FLEISCHNER H,HOBBS A M.Hamiltonian Total Graphs[J].Math Notes,1975,68:59-82.

MA G Y,WU B Y D R.Hamiltonicity of complements of total graphs[J].Lecture Notes in Comput Sci,2007,4381:109-119.

XU L,WU B Y D R.Transformation graph G-+-[J].Discrete Math,2008,308:5144-5148.

ZHEN L Y,WU B Y D R.Hamiltonicity of transformation graph G+--[J].Ars Combin,2013,108:117-127.

YI L,WU B Y D R.The transformation graph G++-[J].Australas J Combin,2009,44:37-42.

SIM?OES-PEREIRA J M S.Connectivity,Line-Connectivity and J-Connection of the Total Graph[J].Math Ann,1972,196:48-57.

HAMADA T,NONAKA T,YOSHIMURA I.On the connectivity of total graphs[J].Math Ann,1972,196:30-38.

BAUER D,TINDELL R.The Connectivities of Line and Total Graphs[J].J Graph Theory,1982,197-203.

ZHANG Z,HUANG X H.Connectivity of transformation graph G+-+[J].Graph Theory Notes of New York,2002,43:35-38.

CHEN J Y,MENG J X.Super edge-connectivity of two classes of transformation graphs[D].Urumqi:Xinjiang University,2006.

CHEN J Y,MENG J X.Super edge-connectivity of transformation graph G--+[J].Journal of Shaanxi Normal University (Natural Science Edit ion),2006,34(1):123-124.

CHEN J Y,MENG J X.Super edge-connectivity of transformation graphs G++-[J].Journal of Xinjiang University(Natural Science Edition),2006,23(1):1-4.

CHEN J Y,MENG J X.Maximal edge-connectivity of transformation graphs G+--[J].J East China Norm Univ Natur Sci Ed,2006,5:83-86.

CHEN J Y,ZHOU J,HUANG L H.Maximal edge-connectivity of transformation graphs G-+-[J].J Lanzhou Univ Natur Sci Ed,2009,3:104-107.

WANG B,ZHANG Z.On cyclic edge connectivity of transitive graphs[J].Discrete Mathematics,2009,309(13):4555-4563.

CHEN J Y,ZHU W H,JIANG B H.Cyclic edge-connectivity of transformation graph G++-[J].J Lanzhou Univ Natur Sci Ed,2016,52(3):393-395+404.

GUTMAN I,TRINAJSTIC N.Graph theory and molecular orbitals,Totalπ-electron energy of alternant hydrocarbons[J].Chem Phys Lett,1972,17:535-538.

ASHRAFI A R,DOˇSLI′C T,HAMZEH A.The Zagreb coindices of graph operations[J].Discrete Appl Math,2010,158:1571-1578.

DE N.F-index of Total Transformation Graphs[J].ar Xiv,2016:1-10.

HOSAMANI S M,GUTMAN I.Zagreb indices of transformation graphs and total transformation graphs[J].Applied Mathematics and Computation,2014,247:1156-1160.

FURTULA B,GUTMAN I.A forgotten topological index[J].J Math Chem,2015,53(4):1184-1190.

RANJINI P S,LOKESHA V,USHA A.Relation between phenylene and hexagonal squeeze using harmonic index[J].International Journal of Graph Theory,2013,1:116-121.

NARUMI H,KATAYAMA M.Simple topological index.A newly devised index characterizing the topological nature of structural isomers of saturated hydrocarbons[J].Mem Fac Eng Hokkaido Univ,1984,16:209-214.

TOMOVICˇZ,GUTMAN I.Narumi-Katayama index of phenylenes[J].J Serb Chem Soc,2001,66(4):243-247.

ELIASI M,IRANMANESH A,GUTMAN I.Multiplicative versions of first Zagreb index[J].MATCH Commun Math Comput Chem,2012,68:217-230.

DE N.Narumi-Katayama index of total transformation graphs[J].Discrete Mathematics Algorithms and Applications,2017,9(3):1750033.

CVETKOVI′C D M,DOOB M,SACHS H.Spectra of graphs:theory and applications[M].Heidelberg Leipzig:Johann Ambrosius Barth Verlag,1995.

YAN J,XU K X.Spectra of transformation graphs of a regular graph[J].Appl Math J Chinese Univ Ser A,2008,23(4):476-480.

DENG A P,KELMANS A,MENG J X.Laplacian spectra of regular graph transformations[J].Discrete Appl Math,2013,161:118-133.

MITCHELL S,HEDETNIEMI S T.Edge domination in trees[J].Congr Numer,1977,19:489-509.

SAMPATHKUMAR E,LATHA L P.Strong (weak) domination and domination balance in graph[J].Discrete Mathematics,1996,161:235-242.

AYTAC?A,TURACI T.Vulnerability Measures of Transformation Graph Gxy+[J].International Journal of Foundations of Computer Science,2015,26(6):667-675.

JEBITHA M K A,JOSEPH J P.Domination in transformation graph G+-+[J].International J Math Combin,2011,1:58-73.

JEBITHA M K A,JOSEPH J P.Domination in transformation graph G-+-[J].Journal of Discrete Mathematical Sciences and Cryptography,2011,14(3):279-303.

Views

下载量

CSCD

Alert me when the article has been cited

提交

Tools

Publicity Resources

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)

Related Author

刘振华

黄晓晖

刘晓平

马国燕

Related Institution

No data

⁰

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