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Hamiltonicity of Complements of Total Graphs

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Discrete Geometry, Combinatorics and Graph Theory (CJCDGCGT 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4381))

Abstract

For a graph G, the total graph T(G) of G is the graph with vertex set V(G) ∪ E(G) in which the vertices x and y are joined by an edge if x and y are adjacent or incident in G. In this paper, we show that the complement of total graph T(G) of a simple graph G is hamiltonian if and only if G is not isomorphic to any graph in {K 1, r | r ≥ 1} ∪ {K 1, s  + K 1| s ≥ 1} ∪ {K 1, t  + e| t ≥ 2} ∪ {K 2 + 2K 1, K 3 + ,K 1, K 3 + 2K 1, K 4}.

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Authors and Affiliations

  1. College of Mathematics and System Science, Xinjiang University, Urumqi, Xinjiang, 830046, P.R. China

    Guoyan Ma & Baoyindureng Wu

Authors
  1. Guoyan Ma
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  2. Baoyindureng Wu
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Jin Akiyama William Y. C. Chen Mikio Kano Xueliang Li Qinglin Yu

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Ma, G., Wu, B. (2007). Hamiltonicity of Complements of Total Graphs. In: Akiyama, J., Chen, W.Y.C., Kano, M., Li, X., Yu, Q. (eds) Discrete Geometry, Combinatorics and Graph Theory. CJCDGCGT 2005. Lecture Notes in Computer Science, vol 4381. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70666-3_12

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  • DOI: https://doi.org/10.1007/978-3-540-70666-3_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-70665-6

  • Online ISBN: 978-3-540-70666-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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