Professor Cayley

Cayley graphs - Cayley nets

It is, however, not clear how to choose the generators to produce special graphs. We know many topologies and their generators, but many more may be constructed in the future, having better properties (in terms of diameter, nodal degree and connectivity) than for instance the hypercube. I will present several graphs which connect rings using the generator g 1 and some additional generators.

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...

Winsor , Major Professor Albert Choi , Minor Professor

Cayley Hypersurfaces

This is the Cayley surface when N = 3. The next few are as follows. x4 = x1x3 + 1 2 x2 2 − x1 x2 + 1 4 x1 4 x5 = x1x4 + x2x3 − x1 x3 − x1x2 2 + x1 x2 − 1 5 x1 5 x6 = x1x5 + x2x4 + 1 2 x3 2 − x1 x4 − 2x1x2x3 − 1 3 x2 3 + x1 x3 + 3 2 x1 x2 2 − x1 x2 + 1 6 x1 . Since the first term in (1) is −xN and this is the only occurrence of this variable, these hypersurfaces are polynomial graphs over the re...

Cayley Graphs

keywords: Cayley graphs, groups, visualizations, proofs.