Groupoids of homogenous factorisation of graphs

Abstract

This thesis is study on confluence of algebraic structures and graph theory. Its aim is to consider groupoids from factorisation of complete graphs. We are especially interested in the case where the factors are isomorphic. We analyse the loops obtained from homogenous factorisation and ask if homogeneity is reflected in the kind of loops that are obtained. In particular we interested to see if we obtain either groups or quasi-associative Cayley sets from these loops