An infinite family of octahedral crossing numbers | Zendy

Gross Jonathan L. | Zendy

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An infinite family of octahedral crossing numbers

Author(s) -

Gross Jonathan L.

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.3190020211

Subject(s) - combinatorics , mathematics , vertex (graph theory) , modulo , octahedron , graph , crossing number (knot theory) , discrete mathematics , crystallography , chemistry , intersection (aeronautics) , crystal structure , engineering , aerospace engineering

This paper calculates some crossing numbers for certain octahedral graphs. Precisely, if the number p is a prime power congruent to 1 modulo 4, then the crossing number of the p ‐dimensional octahedral graph in the orientable surface of genus ( p –1)( p ‐4)/4 is (p 2 –p)/2. The key step is the construction of a self‐dual imbedding of the complete graph on p vertices such that no face boundary contains a repeated vertex.

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