The tools we use include graph theory and linear algebra. Call this automorphism a j . The normal circulant graphs that can also be represented as Cayley graphs on some non-cyclic group of order n are characterised. This result is compared with other results on graphs that can be represented as Cayley graphs on distinct groups of order n . This is based on joint work with Dr. Dragan Marusic of the University of Ljubljana.
G is well-covered if the sum of the weights is the same for each maximal independent set of G .
Caro et al. show that well-covered weightings form a vector space. G is a collection of cycles, C , such that every edge of G lies in precisely two cycles of C . Both the CDC Conjecture and the SCDC Conjecture have been verified for various classes of graphs, but remain open in general. The structure that is inherent in graph products makes such graphs ideal special cases for which to verify the SCDC Conjecture. There are various graph products that can be considered, and in this talk I will describe some results and techniques for proving the SCDC Conjecture for certain graph products.