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A296525 Maximal diameter of connected k-regular graphs on 2*n nodes written as array T(n,k), 2 <= k < 2*n. 6

%I #23 Dec 20 2017 14:44:43

%S 2,1,3,2,2,1,4,3,2,2,2,5,5,3,2,2,2,2,1,6,6,4,3,2,2,2,2,2,1,7,8,5,5,3,

%T 2,2,2,2,2,2,1,8,9,7,5

%N Maximal diameter of connected k-regular graphs on 2*n nodes written as array T(n,k), 2 <= k < 2*n.

%C The results were found by applying the Floyd-Warshall algorithm to the output of Markus Meringer's GenReg program.

%H L. Caccetta, W. F. Smyth <a href="https://doi.org/10.1016/0012-365X(92)90047-J">Graphs of maximum diameter</a>, Discrete Mathematics, Volume 102, Issue 2, 20 May 1992, Pages 121-141.

%H M. Meringer, <a href="http://www.mathe2.uni-bayreuth.de/markus/reggraphs.html">Regular Graphs.</a>

%H M. Meringer, <a href="https://sourceforge.net/projects/genreg/">GenReg</a>, Generation of regular graphs.

%H StackOverflow, <a href="https://stackoverflow.com/questions/15646307/algorithm-for-diameter-of-graph">Algorithm for diameter of graph?</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Distance_(graph_theory)">Distance (graph theory).</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Floyd%E2%80%93Warshall_algorithm">Floyd-Warshall algorithm.</a>

%e Table starts:

%e Degree = 2 3 4 5 6 7 8 9

%e n= 4 : 2 1

%e n= 6 : 3 2 2 1

%e n= 8 : 4 3 2 2 2 1

%e n=10 : 5 5 3 2 2 2 2 1

%e ...

%e See example in A296526 for a complete illustration of the irregular table.

%Y Cf. A068934, A294732 (2nd column of table), A294733, A296524, A296526, A296621.

%K nonn,tabf,more,hard

%O 2,1

%A _Hugo Pfoertner_, Dec 14 2017

%E a(46) corresponding to the quintic graph on 16 nodes from _Hugo Pfoertner_, Dec 19 2017

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Last modified July 26 00:14 EDT 2024. Contains 374615 sequences. (Running on oeis4.)