Accession Number : AD0771470

Title :   6-Valent Analogues of Eberhard's Theorem.

Descriptive Note : Technical rept.,

Corporate Author : WASHINGTON UNIV SEATTLE DEPT OF MATHEMATICS

Personal Author(s) : Zaks,Joseph

Report Date : NOV 1973

Pagination or Media Count : 18

Abstract : If (p sub j) denotes the number of j-gonal faces of a planar map, it follows from Euler's theorem that the summation from j = 1 of (3 - j)(p sub j) = 6 for every connected 6-valent graph. It is proved that, conversely, given any sequence (p1,p2,...,pn) of non-negative integers satisfying this equation, there exists a connected 6-valent planar graph that has precisely (p sub j) j-gonal faces for each j not = 3. Also established is the analogous result for graphs having a 2-cell imbedding in the torus. (Author)

Descriptors :   *Graphics, Theorems

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE