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Arc-transitive homogeneous factorizations and affine planes

โœ Scribed by Tian Khoon Lim

Publisher
John Wiley and Sons
Year
2006
Tongue
English
Weight
140 KB
Volume
14
Category
Article
ISSN
1063-8539

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โœฆ Synopsis

Abstract

We study arcโ€transitive homogeneous factorizations of a complete graph on 81 vertices and give an almost complete description of all possible factors that arise. In particular, we show that there exists an arcโ€transitive homogeneous factorization of K~81~ such that the factors are isomorphic to the Hamming graph H(9,2). This gives rise to an edge partition of K~81~ into 90 copies of K~9~ and it turns out that these copies of K~9~ form the blocks of the exceptional nearfield affine plane of order 9. ยฉ 2005 Wiley Periodicals, Inc. J Combin Designs 14: 290โ€“300, 2006

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