21 citations · 68 across the 14 of their papers we have counts for
17 papers
New constructions of free products and geodetic Cayley graphs
Joshua Abraham, Murray Elder, Adam Piggott +1
A connected graph is called \emph{geodetic} if there is a unique shortest path between each pair of vertices. We introduce a systematic method for constructing new presentations of…
Finite groups with geodetic Cayley graphs
Murray Elder, Adam Piggott, Florian Stober +2
A connected undirected graph is called \emph{geodetic} if for every pair of vertices there is a unique shortest path connecting them. It has been conjectured that for finite groups…
Graphs and groups with unique geodesics
Murray Elder, Giles Gardam, Adam Piggott +2
A connected graph is called \emph{geodetic} if there is a unique geodesic between each pair of vertices. In this paper we prove that if a finitely generated group admits a Cayley g…
On -geodetic graphs and groups
Murray Elder, Adam Piggott, Kane Townsend
We call a graph -geodetic, for some , if it is connected and between any two vertices there are at most geodesics. It is shown that any hyperbolic group with a -…
The isomorphism problem for plain groups is in
Heiko Dietrich, Murray Elder, Adam Piggott +2
Testing isomorphism of infinite groups is a classical topic, but from the complexity theory viewpoint, few results are known. S{é}nizergues and the fifth author (ICALP2018) proved…
On groups presented by inverse-closed finite convergent length-reducing rewriting systems
Murray Elder, Adam Piggott
We show that groups presented by inverse-closed finite convergent length-reducing rewriting systems are characterised by a striking geometric property: their Cayley graphs are geod…