3 citations · 4 across the 7 of their papers we have counts for
8 papers
Fragments in symmetric configurations with block size 3
Grahame Erskine, Terry Griggs, Jozef Širáň
We begin the study of collections of three blocks which can occur in a symmetric configuration with block size 3, . Formulae are derived for the number of occurrences of these…
On networks with order close to the Moore bound
James Tuite, Grahame Erskine
The degree/diameter problem for mixed graphs asks for the largest possible order of a mixed graph with given diameter and degree parameters. Similarly the \emph{degree/geodecity} p…
Colouring problems for symmetric configurations with block size 3
Grahame Erskine, Terry Griggs, Jozef Širáň
The study of symmetric configurations with block size 3 has a long and rich history. In this paper we consider two colouring problems which arise naturally in the study of th…
On the upper embedding of symmetric configurations with block size 3
Grahame Erskine, Terry Griggs, Jozef Širáň
We consider the problem of embedding a symmetric configuration with block size 3 in an orientable surface in such a way that the blocks of the configuration form triangular faces a…
Graphs derived from perfect difference sets
Grahame Erskine, Peter Fratrič, Jozef Širáň
We study a family of graphs with diameter two and asymptotically optimal order for their maximum degree, obtained from perfect difference sets. We show that for all known examples…
On total regularity of mixed graphs with order close to the Moore bound
James Tuite, Grahame Erskine
The undirected degree/diameter and degree/girth problems and their directed analogues have been studied for many decades in the search for efficient network topologies. Recently su…