Minimal Embedding of Hypercubic Graphs on Surface

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

Abstract

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 .

Keywords

Standard Form Planar Graph Complete Graph Binary Sequence Complete Bipartite Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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