Isographs and oriented isographs

Abstract

An algorithm, based on a weighted form of Burnside's lemma, is presented for the enumeration of isographs and oriented isographs. In the two-stage algorithm, the contributions to the sum of weights from different cycles and cycle pairs of the underlying group are first listed and then ‘multiplied’ by a stagewise process. The elimination of the unwanted graphs in the different stages ensures that the computations are kept to the minimum. Particular results obtained include self-converse and self-complementary isographs and oriented isographs. Eulerian digraphs, etc. are then obtained by applying the Möbius inversion formula.