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The transformation graph G(xyz) when xyz=-++
Wu, B; Zhang, L; Zhang, Z
2005-07-06
Source PublicationDISCRETE MATHEMATICS
ISSN0012-365X
Volume296Issue:2-3Pages:263-270
AbstractThe transformation graph G(-++) of G is the graph with vertex set V(G) U E(G) in which the vertex x and y are joined by an edge if one of the following conditions holds: (i) x, y is an element of V (G), and x and y are not adjacent in G, (ii) x, y is an element of E(G), and x and y are adjacent in G, (iii) one of x and y is in V(G) and the other is in E(G), and they are incident in G. In this paper, it is shown that for two graphs G and G', G(-++) congruent to G'(-++) if and only if G congruent to G'. Simple necessary and sufficient conditions are given for G(-++) to be planar and hamiltonian, respectively. It is also shown that for a graph G, the edge-connectivity of G(-++) is equal to its minimum degree. Two related conjectures and some research problems are presented. (c) 2005 Elsevier B.V. All rights reserved.
Keywordtransformation total graph isomorphism
DOI10.1016/j.disc.2005.04.002
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000231030700011
PublisherELSEVIER SCIENCE BV
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/1688
Collection中国科学院数学与系统科学研究院
Corresponding AuthorWu, B
Affiliation1.Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830046, Xinjiang, Peoples R China
2.Chinese Acad Sci, Inst Syst Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China
Recommended Citation
GB/T 7714
Wu, B,Zhang, L,Zhang, Z. The transformation graph G(xyz) when xyz=-++[J]. DISCRETE MATHEMATICS,2005,296(2-3):263-270.
APA Wu, B,Zhang, L,&Zhang, Z.(2005).The transformation graph G(xyz) when xyz=-++.DISCRETE MATHEMATICS,296(2-3),263-270.
MLA Wu, B,et al."The transformation graph G(xyz) when xyz=-++".DISCRETE MATHEMATICS 296.2-3(2005):263-270.
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