Minimal Embedding of Hypercubic Graphs on Surface

  • Kazuaki Kobayashi
  • Takako Kodate
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7033)


In this paper, we propose a minimal embedding of a non-planar, n-dimensional hypercubic graph on a surface as a “standard” embedding. The “standard” form of embedding graph on a surface has been understudied and therefore, has remained undefined. The aim of this paper is to define what the “standard form” is for a non-planar graph, while distinguishing different embedding patterns of a graph. As a result, we defined a value ω(G) for all non-planar graphs G, and determined the value ω(Q n ) for n-dimensional hypercubic graphs denoted by Q n .


Standard Form Planar Graph Complete Graph Binary Sequence Complete Bipartite Graph 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Kazuaki Kobayashi
    • 1
  • Takako Kodate
    • 1
  1. 1.Tokyo Woman’s Christian UniversitySuginami-kuJapan

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