22 citations · 46 across the 20 of their papers we have counts for
24 papers
Automorphisms of pentagonal geometries with block size 3
Grahame Erskine, Terry S. Griggs
A pentagonal geometry PENT(k,r) is a k-uniform, r-regular partial linear space with the property that the set of points not collinear with a given point x is itself a line in the g…
Vertex-transitive closures of graphs
Martin Bachratý, Grahame Erskine, Štefánia Glevitzká +2
A vertex-transitive closure of is a vertex-transitive supergraph of on the same vertex set. The vertex-transitive number of a graph , denoted by , is the smal…
Cycle switching in Steiner triple systems of order 19
Grahame Erskine, Terry S. Griggs
Cycle switching is a particular form of transformation applied to isomorphism classes of a Steiner triple system of a given order (an ), yielding another . This…
Properties of Steiner triple systems of order 21
Grahame Erskine, Terry S. Griggs
Properties of the 62,336,617 Steiner triple systems of order 21 with a non-trivial automorphism group are examined. In particular, there are 28 which have no parallel class, six th…
On large regular (1,1,k)-mixed graphs
C. Dalfó, G. Erskine, G. Exoo +4
An -mixed graph has every vertex with undirected degree , directed in- and out-degree , and diameter . In this paper, we study the case , proposing som…
Mutually avoiding Eulerian circuits
Grahame Erskine, Terry Griggs, Robert Lewis +1
Two Eulerian circuits, both starting and ending at the same vertex, are avoiding if at every other point of the circuits they are at least distance 2 apart. An Eulerian graph which…
On the Vertex Position Number of Graphs
Maya Thankachy, Elias John Thomas, Ullas Chandran +3
In this paper we generalise the notion of visibility from a point in an integer lattice to the setting of graph theory. For a vertex of a connected graph , we say that a set…
Good point sequencings of Steiner triple systems
Grahame Erskine, Terry Griggs
An l-good sequencing of a Steiner triple system of order v, STS(v), is a permutation of the points of the system such that no l consecutive points in the permutation contains a blo…
Small graphs and hypergraphs of given degree and girth
Grahame Erskine, James Tuite
The search for the smallest possible -regular graph of girth has a long history, and is usually known as the cage problem. This problem has a natural extension to hypergraph…
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…
Clique-partitioned graphs
Grahame Erskine, Terry Griggs, Jozef Širáň
A graph of order where and is said to be weakly -clique-partitioned if its vertex set can be decomposed in a unique way into vertex-disjoint…
Self-dual, self-Petrie-dual and Möbius regular maps on linear fractional groups
Grahame Erskine, Katarína Hriňáková, Olivia Jeans
Regular maps on linear fractional groups and ) have been studied for many years and the theory is well-developed, including generating sets for the asscoiated g…
Mixed Moore Cayley graphs
Grahame Erskine
The degree-diameter problem seeks to find the largest possible number of vertices in a graph having given diameter and given maximum degree. There has been much recent interest in…
Large Cayley graphs of small diameter
Grahame Erskine, James Tuite
The degree-diameter problem seeks to find the largest possible number of vertices in a graph having given diameter and given maximum degree. Very often the problem is studied for r…
Orientably-regular maps on twisted linear fractional groups
Grahame Erskine, Katarína Hriňáková, Jozef Širáň
We present an enumeration of orientably-regular maps with automorphism group isomorphic to the twisted linear fractional group for any odd prime power .
Groups whose locally maximal product-free sets are complete
Chimere S. Anabanti, Grahame Erskine, Sarah B. Hart
Let be a finite group and a subset of . Then is product-free if , and complete if . A product-free set is locall…
A revised Moore bound for mixed graphs
Dominique Buset, Mourad El Amiri, Grahame Erskine +2
The degree-diameter problem seeks to find the maximum possible order of a graph with a given (maximum) degree and diameter. It is known that graphs attaining the maximum possible v…
Large circulant graphs of fixed diameter and arbitrary degree
David Bevan, Grahame Erskine, Robert Lewis
We consider the degree-diameter problem for undirected and directed circulant graphs. To date, attempts to generate families of large circulant graphs of arbitrary degree for a giv…
Diameter 2 Cayley Graphs of Dihedral Groups
Grahame Erskine
We consider the degree-diameter problem for Cayley graphs of dihedral groups. We find upper and lower bounds on the maximum number of vertices of such a graph with diameter 2 and d…