TOROIDAL AND PROJECTIVE CYCLIC GRAPHS

Abstract

All finite groups with toroidal or projective cyclic graphs are classified. Indeed, it is shown that the only finite groups with projective cyclic graphs are S3 × Z2, D14, QD16 and <x, y : x^7 = y^3 = 1; x^y = x^2> which all have toroidal cyclic graph too. Also, D16 is characterized as the only finite group whose cyclic graph is toroidal but not projective