Cayley maps

Regular maps from Cayley graphs, part 1: Balanced Cayley maps

Skoviera, M. and J. ‘&Iii, Regular maps from Cayley graphs, Part i: Balanced Cayley maps, Discrete Mathematics IO9 (1992) 265-276. A Cayley map is a Cayley graph 2-cell embedded in some orientable surface so that the local rotations at every vertex are identical. Two types of Cayley maps are introduced: the balanced and antibalanced Cayley maps. In Part 1, conditions are given uuder which a bal...

The Cayley Isomorphism Property for Cayley Maps

The Cayley Isomorphism property for combinatorial objects was introduced by L. Babai in 1977. Since then it has been intensively studied for binary relational structures: graphs, digraphs, colored graphs etc. In this paper we study this property for oriented Cayley maps. A Cayley map is a Cayley graph provided by a cyclic rotation of its connection set. If the underlying graph is connected, the...

Cayley Maps for Se(3)

The Cayley map for the rotation group SO(3) is extended to a map from the Lie algebra of the group of rigid body motions SE(3) to the group itself. This is done in several inequivalent ways. A close connection between these maps and linear line complexes associated with a finite screw motions is found.

Finite Edge-transitive Cayley Graphs and Rotary Cayley Maps

This paper aims to develop a theory for studying Cayley graphs, especially for those with a high degree of symmetry. The theory consists of analysing several types of basic Cayley graphs (normal, bi-normal, and corefree), and analysing several operations of Cayley graphs (core quotient, normal quotient, and imprimitive quotient). It provides methods for constructing and characterising various c...

Triangular Cayley maps of Kn, n, n