A class of highly symmetric Archdeacon embeddings

2022/12/16 by Costa, Simone, Mella, Lorenzo
#05B20 #05C10 #05C60 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2212.08491

Abstract

Archdeacon, in his seminal paper [1], defined the concept of Heffter array to provide explicit constructions of biembeddings of the complete graph K_v into orientable surfaces, the so-called Archdeacon embeddings, and proved that these embeddings are ℤ_v-regular. In this paper, we show that an Archdeacon embedding may admit an automorphism group that is strictly larger than ℤ_v. Indeed, as an application of the interesting class of arrays recently introduced by Buratti in [2], we exhibit, for infinitely many values of v, an embedding of this type having full automorphism group of size v \choose 2 that is the largest possible one.

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