Hamiltonicity of complements of total graphs

  • Authors:

  • Guoyan Ma;Baoyindureng Wu

  • Affiliations:

  • College of Mathematics and System Science, Xinjiang University, Urumqi, Xinjiang, P.R. China;College of Mathematics and System Science, Xinjiang University, Urumqi, Xinjiang, P.R. China

  • Venue:
  • CJCDGCGT'05 Proceedings of the 7th China-Japan conference on Discrete geometry, combinatorics and graph theory
  • Year:
  • 2005

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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., r| r ≥ 1}∪{K., s+K.| s ≥ 1} ∪ {K.,t + e| t ≥ 2} ∪ {K. + 2K., K. + K., K. + 2K., K.}.