CanaDAM 2015
Université de la Saskatchewan, 1 - 4 juin 2015

Graph theory of Brian Alspach II
Responsable et président: Joy Morris (University of Lethbridge) et Mateja Sajna (University of Ottawa)

KLAVDIJA KUTNAR, University of Primorskem

A graph $X$ is said to be $G$-half-arc-transitive if $G\le Aut(X)$ acts transitively on the set of vertices of $X$ and on the set of edges of $X$ but does not act transitively on the set of arcs of $X$. Such graphs can be studied via corresponding alternets, that is, equivalence classes of the so-called reachability relation. In this talk I will present recent results about graphs admitting a half-arc-transitive group action with at most five alternets.

DRAGAN MARUSIC, University of Primorskem
On the full automorphism group in vertex-transitive graphs  [PDF]

One of the crucial questions in symmetries of graphs is as follows. Given a vertex-transitive graph X admitting a transitive action of a group H, determine whether H is the full automorphism group of the graph X. We will give an overview of the various results relative to the above problem.

DAVE MORRIS, University of Lethbridge
Hamiltonian cycles in some easy Cayley graphs  [PDF]

It was conjectured 45 years ago that every connected Cayley graph has a hamiltonian cycle, but there is very little evidence for such a broad claim. The talk will explain how Cayley graphs are obtained from finite groups, describe progress (including some theorems of Brian Alspach) that has been made by assuming the group is not very complicated, and mention a few of the many open questions.

JOY MORRIS, University of Lethbridge
The Cayley Isomorphism problem  [PDF]

Two Cayley graphs on the same group Cay$(G;S)$ and Cay$(G;S')$ will always be isomorphic if there is a group automorphism $\varphi$ of $G$ such that $\varphi(S)=S'$. If $X$ is a Cayley graph on $G$, and {\it every} \ isomorphic Cayley graph on $G$ can be accounted for in this way (via some group automorphism), then we say that $X$ is a CI-graph. If every Cayley graph on $G$ is a CI-graph, then $G$ is a CI-group. In this talk I will give an overview of the current status of the problem of determining which groups are CI-groups.


Atlantic Association for Research in the Mathematical Sciences Centre de recherches mathmatiques The Fields Institute Pacific Institute for the Mathematical Sciences Socit mathmatique du Canada Université Saskatchewan