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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
##### Keywords:
graph; degree; diameter; Cayley graph; vertex-transitive graph
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##### References:
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