On Regular Cayley Maps with Alternating Power Functions

John Martino1, Paula Smith2
1Western Michigan University
2Ohio Dominican University

Abstract

Two classes of regular Cayley maps, balanced and antibalanced, have long been understood, see \([12,11]\). A recent generalization is that of an e-balanced map, see \([7,2,5,8]\). These maps can be described using the power function introduced in \([4]\); e-balanced maps are the ones with constant power functions on the generating set. In this paper we examine a further generalization to the situation where the power function alternates between two values.