The genus of a complete graph equals the least integer greater than or equal to (E-3V+6)/6, whereE andV are the numbers of edges and vertices of the graph. This paper extends the class of graphs known to have this property, concentrating on graphs whose number of vertices is congruent to 6 modulo 12.
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This research was initiated with partial support from NSF grant GJ-28403 at Columbia University and continued while the author was an IBM Postdoctoral Fellow in the Mathematical Sciences Department at the Thomas J. Watson Research Center, Yorktown Heights, N.Y. The author is also an Alfred P. Sloan Fellow.
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Gross, J.L. The genus of nearly complete graphs-case 6. Aeq. Math. 13, 243–249 (1975). https://doi.org/10.1007/BF01836527
AMS (1970) subject classifications
- Primary 05C10, 55A15
- Secondary 05C25, 55A10