On Arc-Regular Permutation Groups Using Latin Squares

For a given a permutation group G, the problem of determining which regular digraphs admit G as an arc-regular group of automorphism is considered. Groups which admit such a representation can be characterized in terms of generating sets satisfying certain properties, and a procedure to manufacture such groups is presented. The technique is based on constructing appropriate factorizations of (smaller) regular line digraphs by means of Latin squares. Using this approach, all possible representations of transitive groups of degree up to seven as arc-regular groups of digraphs of some degree is presented.