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The Genus of the Coxeter Graph

Published online by Cambridge University Press:  20 November 2018

Jane M. O. Mitchell
Jane M. O. Mitchell*
Affiliation:
Department of Statistics and Modelling Science, University of Strathclyde, Glasgow Gl 1XH, United Kingdom, e-mail:jane@uk.ac.strathclyde.stams
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Abstract

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In [1], Biggs stated that the Coxeter graph can be embedded in an orientable surface of genus 3. The purpose of this note is to point out that Biggs' embedding is in fact into a non-orientable surface. Further, it is shown that the orientable genus is 3 and the non-orientable genus is 6.

Keywords

05C10
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 38 , Issue 4 , 01 December 1995 , pp. 462 - 464
Copyright
Copyright © Canadian Mathematical Society 1995

References

1. Biggs, N., Three remarkable graphs, Canad. J. Math. 25(1973), 397–411.Google Scholar
2. Brouwer, A. E., Cohen, A. M. and Neumaier, A., Distance-Regular Graphs, Springer-Verlag, New York, Berlin, Heidelberg, 1989, 382–383.Google Scholar
3. Coxeter, H. S. M., My graph, Proc. London Math. Soc. 46(1983), 117–136.Google Scholar