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- Dominique Buset, Mourad El Amiri, Grahame Erskine, Mirka Miller, Hebert Pérez-Rosés
- Discrete Mathematics
- 2016

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 value (the Moore bound) are extremely rare, but much activity is focussed on finding new examples of graphs or families of graph with orders approaching the bound as closely as… (More)

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 given diameter have concentrated mainly on the diameter 2 case. We present a direct product construction yielding improved bounds for small diameters and introduce a new general… (More)

- Grahame Erskine
- Discrete Mathematics
- 2015

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 degree d. We completely determine the asymptotic behaviour of this class of graphs by showing that both limits are asymptotically d/2.

Let G be a finite group and S a subset of G. Then S is product-free if S ∩ SS = ∅, and complete if G∗ ⊆ S ∪ SS. A product-free set is locally maximal if it is not contained in a strictly larger product-free set. If S is product-free and complete then S is locally maximal, but the converse does not necessarily hold. Street and Whitehead [11] defined a group… (More)

- H. Lipps, G. A. Erskine
- SGNM
- 1985

Dongarra et al have recently proposed extensions to the subprogram package BLAS to improve the performance of more elaborate linear algebra codes such as LINPACK. (See [2] - [4]) We summarize here our experience with a similar project.

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