Skip to content

Toggle service links

You are here

  1. Home
  2. Dr Grahame Erskine

Dr Grahame Erskine

Profile summary

Professional biography

After an undergraduate degree in Mathematics from the University of Aberdeen, I embarked on a career in IT development in a major UK financial services firm. In 2010 I returned to mathematics part-time via the OU's MSc programme. After graduating with an MSc I stayed on at the OU full-time to complete a PhD in algebraic graph theory.

I am currenly a visiting research fellow in the School of Mathematics and Statistics.

Research interests

My research interests are principally in algebraic graph theory and related areas of combinatorics such as incidence structures.

Specifically, I am interested in the degree-diameter and degree-girth problems for graphs, together with related notions in digraphs and mixed graphs.


Clique-partitioned graphs (2022-06-15)
Erskine, Grahame; Griggs, Terry and Širáň, Jozef
Discrete Applied Mathematics, 314 (pp. 238-248)

Colouring problems for symmetric configurations with block size 3 (2021-06)
Erskine, Grahame; Griggs, Terry and Širáň, Jozef
Journal of Combinatorial Designs, 29(6) (pp. 397-423)

Graphs derived from perfect difference sets (2021)
Erskine, Grahame; Fratrič, Peter and Širáň, Jozef
Australasian Journal of Combinatorics, 80(1) (pp. 48-56)

Self-dual, self-Petrie-dual and Möbius regular maps on linear fractional groups (2020-08-26)
Erskine, Grahame; Hriňáková, Katarína and Jeans, Olivia
The Art of Discrete and Applied Mathematics, 3, Article 3(1)

On the upper embedding of symmetric configurations with block size 3 (2020-04)
Erskine, Grahame; Griggs, Terry and Širáň, Jozef
Discrete Mathematics, 343, Article 111774(4)

On Total Regularity of Mixed Graphs with Order Close to the Moore Bound (2019)
Tuite, James and Erskine, Grahame
Graphs and Combinatorics, 35 (pp. 1253-1272)

Large Cayley graphs of small diameter (2018-12-11)
Erskine, Grahame and Tuite, James
Discrete Applied Mathematics, 250 (pp. 202-214)

Groups whose locally maximal product-free sets are complete (2018-05-10)
Anabanti, Chimere S.; Erskine, Grahame and Hart, Sarah B.
Australasian Journal of Combinatorics, 71(3) (pp. 544-563)

Mixed Moore Cayley Graphs (2017-12-18)
Erskine, Grahame
Journal of Interconnection Networks, 17, Article 1741010(03n04)

Large circulant graphs of fixed diameter and arbitrary degree (2017)
Bevan, David; Erskine, Grahame and Lewis, Robert
Ars Mathematica Contemporanea, 13(2) (pp. 275-291)

A revised Moore bound for mixed graphs (2016-08-06)
Buset, Dominique; El Amiri, Mourad; Erskine, Grahame; Miller, Mirka and Pérez-Rosés, Hebert
Discrete Mathematics, 339(8) (pp. 2066-2069)

Diameter 2 Cayley graphs of dihedral groups (2015-02-14)
Erskine, Grahame
Discrete Mathematics, 338(6) (pp. 1022-1024)

Orientably-regular maps on twisted linear fractional groups (2020-01-11)
Erskine, Grahame; Hriňáková, Katarína and Širáň, Jozef
In: Jones, Gareth A; Ponomarenko, Ilya and Širáň, Jozef eds. Isomorphisms, Symmetry and Computations in Algebraic Graph Theory. PROMS (pp. 1-35)
ISBN : 978-3-030-32808-5, 978-3-030-32807-8 | Publisher : Springer, Cham

New Bounds on k-Geodetic Digraphs and Mixed Graphs (2021)
Tuite, James and Erskine, Grahame
In : Extended Abstracts EuroComb 2021: European Conference on Combinatorics, Graph Theory and Applications (6-10 Sep 2021, Barcelona (Online)) (pp. 778-783)

Diameter, Girth And Other Properties Of Highly Symmetric Graphs (2017-05-12)
Erskine, Grahame
PhD thesis The Open University