Vertex-minimal graphs with dihedral symmetry I

Abstract Let D 2 n denote the dihedral group of order 2 n , where n ≥ 3 . In this article, we build upon the findings of Haggard and McCarthy who, for certain values of n , produced a vertex-minimal graph with dihedral symmetry. Specifically, Haggard considered the situation when n 2 or n is a prime power, and McCarthy investigated the case when n is not divisible by 2 , 3 or 5 . In this article, we assume n is not divisible by 4 and construct a vertex-minimal graph whose automorphism group is isomorphic to D 2 n .