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The genus of the n-octahedron: Regular cases

✍ Scribed by Mark Jungerman; Gerhard Ringel

Publisher: John Wiley and Sons
Year: 1978
Tongue: English
Weight: 284 KB
Volume: 2
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.3190020109

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✦ Synopsis

Abstract

The n‐octahedron O~n~, also denoted K(2,2, …, 2) or K~n(2)~, is the complete n‐partite graph with two vertices in each partite set. The formula
for the (orientable) genus of O~n~ is conjectured for all n and proved for n ≠ (mof 3). Triangular embeddigns are possible precisely when n ≠ 2 (mod 3), and the formula is established by exhibiting such embeddings.

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