Characterising CCA Sylow cyclic groups whose order is not divisible by four

Open access, licensed under Creative CommonsA Cayley graph on a group G has a natural edge-colouring. We say that such a graph is CCA if every automorphism of the graph that preserves this edge-colouring is an element of the normaliser of the regular representation of G. A group G is then said to be CCA if every connected Cayley graph on G is CCA. Our main result is a characterisation of non-CCA graphs on groups that are Sylow cyclic and whose order is not divisible by four. We also provide several new constructions of non-CCA graphs.Ye

Finding CCA groups and graphs algorithmically

Given a group G, any subset C of G\{e} induces a Cayley graph, Cay(G,C). The set C also induces a natural edge-colouring of this graph. All affine automorphisms of the Cayley graph preserve this edge-colouring. A Cayley graph Cay(G,C) has the Cayley Colour Automorphism Property (is CCA), if all its colour-preserving automorphisms are affine. A group G is CCA if every connected Cayley graph on G is CCA. The goal of this thesis is to classify all groups of ‘small’ order to determine if they are CCA. In order to do this, we have developed two main algorithms that are the new contributions of this thesis. One algorithm finds all minimal generating sets for any group. The other algorithm uses this to test whether or not a group is CCA. These algorithms can also be used to determine whether or not a given Cayley graph is CCA.NSERC Canada Graduate Sholarships-Master's Program PIMS-Alberta Graduate Excellence Fellowshi

Mathematical surfaces models between art and reality

In this paper, I want to document the history of the mathematical surfaces models used for the didactics of pure and applied “High Mathematics” and as art pieces. These models were built between the second half of nineteenth century and the 1930s. I want here also to underline several important links that put in correspondence conception and construction of models with scholars, cultural institutes, specific views of research and didactical studies in mathematical sciences and with the world of the figurative arts furthermore. At the same time the singular beauty of form and colour which the models possessed, aroused the admiration of those entirely ignorant of their mathematical attraction