The transformation graph G(xyz) when xyz=-++
Wu, B; Zhang, L; Zhang, Z
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
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000231030700011
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Document Type期刊论文
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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