Jana Siagiová

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For any d ≥ 5 and k ≥ 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, for all sufficiently large d and k, our family gives the current largest known Cayley graphs of degree d and diameter k.
Let ) 2 , (d C , ) 2 , (d AC , and ) 2 , (d CC be the largest order of a Cayley graph of a group, an Abelian group, and a cyclic group, respectively, of diameter 2 and degree d. The currently known best lower bounds on these parameters are 2 / ) 1 ( ) 2 , ( 2   d d C for degrees 1 2   q d where q is an odd prime power, ) 4 )( 8 / 3 ( ) 2 , ( 2   d d(More)
In a mixed (Δ, d)-regular graph, every vertex is incident with Δ ≥ 1 undirected edges and there are d ≥ 1 directed edges entering and leaving each vertex. If such a mixed graph has diameter 2, then its order cannot exceed (Δ+ d) + d+1. This quantity generalizes the Moore bounds for diameter 2 in the case of undirected graphs (when d = 0) and digraphs (when(More)