Arc‐transitive homogeneous factorizations and affine planes

Abstract

AbstractWe study arc‐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 arc‐transitive homogeneous factorization of K81 such that the factors are isomorphic to the Hamming graph H(9,2). This gives rise to an edge partition of K81 into 90 copies of K9 and it turns out that these copies of K9 form the blocks of the exceptional nearfield affine plane of order 9. © 2005 Wiley Periodicals, Inc. J Combin Designs 14: 290–300, 2006