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A344517 Minimum diameter of 4-regular circulant graphs of order n.

%I A344517 #20 Jun 13 2021 03:33:50
%S A344517 1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,
%T A344517 4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,
%U A344517 6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7
%N A344517 Minimum diameter of 4-regular circulant graphs of order n.
%D A344517 F. Boesch and Jhing-Fa Wang, Reliable circulant networks with minimum transmission delay, IEEE Transactions on Circuits and Systems, vol. 32, no. 12, pp. 1286-1291, December 1985, doi: 10.1109/TCS.1985.1085667.
%D A344517 Bevan, David et al. Large circulant graphs of fixed diameter and arbitrary degree. Ars Math. Contemp. 13 (2017): 275-291.
%H A344517 R. Feria-Puron, H. Perez-Roses, and J. Ryan, <a href="http://arxiv.org/abs/1503.07357">Searching for Large Circulant Graphs</a>, arXiv:1503.07357 [math.CO], 2015.
%H A344517 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphDiameter.html">Graph Diameter</a>
%H A344517 Wikipedia, <a href="https://en.wikipedia.org/wiki/Circulant_graph">Circulant Graph</a>
%F A344517 a(n) = ceiling((sqrt(2n-1)-1)/2).
%t A344517 mindiameter[n_]:=Module[{nmax,tab,stab},
%t A344517 nmax=Floor[n/2];
%t A344517 tab=Flatten[#,1]&@Table[Table[{n,i,j,GraphDiameter[CirculantGraph[n,{i,j}]]},{i,1,j-1}],{j,2,nmax}];
%t A344517 stab=Sort[tab,#1[[4]]<#2[[4]]&];
%t A344517 stab[[1]][[4]]//Return]
%t A344517 Table[mindiameter[n],{n,4,120}]
%t A344517 Table[Ceiling[(Sqrt[2n-1]-1)/2],{n,4,88}] (* _Stefano Spezia_, May 23 2021 *)
%Y A344517 Cf. A049287, A075545, A285620.
%K A344517 nonn
%O A344517 4,3
%A A344517 _Andres Cicuttin_, May 21 2021