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Large Cayley graphs and vertex-transitive non-Cayley graphs of given degree and diameter. (English) Zbl 1230.05158
Summary: For any \(d \geq 5\) and \(k \geq 3\) we construct a family of Cayley graphs of degree \(d\), diameter \(k\), and order at least \(k((d - 3)/3)^k\). By comparison with other available results in this area we show that our family gives the largest currently known Cayley graphs for a wide range of sufficiently large degrees and diameters.

MSC:
05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
05C07 Vertex degrees
05C12 Distance in graphs
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