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The genus of a type of graph

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Abstract

Based on the joint tree model introduced by Liu, the genera of further types of graphs not necessary to have certain symmetry can be obtained. In this paper, we obtain the genus of a new type of graph with weak symmetry. As a corollary, the genus of complete tripartite graph K n,n,l (l ⩾ n ⩾ 2) is also derived. The method used here is more direct than those methods, such as current graph, used to calculate the genus of a graph and can be realized in polynomial time.

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Authors and Affiliations

  1. Department of Mathematics, Hebei University of Technology, Tianjin, 300401, China

    ZeLing Shao

  2. Department of Mathematics, Beijing Jiaotong University, Beijing, 100044, China

    YanPei Liu

Authors
  1. ZeLing Shao
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  2. YanPei Liu
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Correspondence to ZeLing Shao.

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Shao, Z., Liu, Y. The genus of a type of graph. Sci. China Math. 53, 457–464 (2010). https://doi.org/10.1007/s11425-009-0078-7

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  • DOI: https://doi.org/10.1007/s11425-009-0078-7

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