Grahame Erskine

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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 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)
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