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The genus of the n ‐octahedron: Regular cases
Author(s) -
Jungerman Mark,
Ringel Gerhard
Publication year - 1978
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.3190020109
Subject(s) - mathematics , combinatorics , octahedron , genus , graph , crystallography , botany , crystal structure , chemistry , biology
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\documentclass{article}\pagestyle{empty}\begin{document}$$ (O_n) = \{ \frac{{(n - 1)(n - 3)}}{3}\} $$\end{document} 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.