Speaker: Jorik Jooken, KU Leuven Kulak Title: On vertex-girth-regular graphs: (Non-)existence, bounds and enumeration Abstract: A vertex-girth-regular vgr(v,k,g,lambda)-graph is a k-regular graph of girth g and order v in which every vertex belongs to exactly lambda cycles of length g. While all vertex-transitive graphs are necessarily vertex-girth-regular, the majority of vertex-girth-regular graphs are not vertex-transitive. Similarly, while many of the smallest k-regular graphs of girth g, the so-called (k,g)-cages, are vertex-girth-regular, infinitely many vertex-girth-regular graphs of degree k and girth…