cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A296620 Number of 4-regular (quartic) connected graphs on n nodes with diameter k written as irregular triangle T(n,k).

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%I A296620 #11 Dec 17 2017 10:06:01
%S A296620 1,0,1,0,2,0,6,0,16,0,24,35,0,37,227,1,0,26,1502,16,0,10,10561,202,5,
%T A296620 0,1,84103,4006,58,0,1,722252,82726,493,19,0,0,6383913,1647078,6224,
%U A296620 202,1,0,0,55831405,30291536,96504,2156,33
%N A296620 Number of 4-regular (quartic) connected graphs on n nodes with diameter k written as irregular triangle T(n,k).
%C A296620 The results were found by applying the Floyd-Warshall algorithm to the output of Markus Meringer's GenReg program.
%H A296620 M. Meringer, <a href="https://sourceforge.net/projects/genreg/">GenReg</a>, Generation of regular graphs.
%H A296620 Wikipedia, <a href="https://en.wikipedia.org/wiki/Distance_(graph_theory)">Distance (graph theory).</a>
%H A296620 Wikipedia, <a href="https://en.wikipedia.org/wiki/Floyd%E2%80%93Warshall_algorithm">Floyd-Warshall algorithm.</a>
%e A296620 Triangle begins:
%e A296620                      Diameter
%e A296620    n/ 1  2        3        4     5    6  7
%e A296620    5: 1
%e A296620    6: 0  1
%e A296620    7: 0  2
%e A296620    8: 0  6
%e A296620    9: 0 16
%e A296620   10: 0 24       35
%e A296620   11: 0 37      227        1x
%e A296620   12: 0 26     1502       16
%e A296620   13: 0 10    10561      202     5
%e A296620   14: 0  1x   84103     4006    58
%e A296620   15: 0  1x  722252    82726   493   19
%e A296620   16: 0  0  6383913  1647078  6224  202  1x
%e A296620   17: 0  0 55831405 30291536 96504 2156 33
%e A296620 .
%e A296620 x indicates provision of adjacency information below.
%e A296620 Examples of unique 4-regular graphs with minimum diameter:
%e A296620 Adjacency matrix of the graph of diameter 2 on 14 nodes:
%e A296620       1 2 3 4 5 6 7 8 9 0 1 2 3 4
%e A296620    1  . 1 1 1 1 . . . . . . . . .
%e A296620    2  1 . . . . 1 1 1 . . . . . .
%e A296620    3  1 . . . . 1 1 1 . . . . . .
%e A296620    4  1 . . . . . . . 1 1 1 . . .
%e A296620    5  1 . . . . . . . . . . 1 1 1
%e A296620    6  . 1 1 . . . . . 1 . . 1 . .
%e A296620    7  . 1 1 . . . . . . 1 . . 1 .
%e A296620    8  . 1 1 . . . . . . . 1 . . 1
%e A296620    9  . . . 1 . 1 . . . . . . 1 1
%e A296620   10  . . . 1 . . 1 . . . . 1 . 1
%e A296620   11  . . . 1 . . . 1 . . . 1 1 .
%e A296620   12  . . . . 1 1 . . . 1 1 . . .
%e A296620   13  . . . . 1 . 1 . 1 . 1 . . .
%e A296620   14  . . . . 1 . . 1 1 1 . . . .
%e A296620 .
%e A296620 Adjacency matrix of the graph of diameter 2 on 15 nodes:
%e A296620       1 2 3 4 5 6 7 8 9 0 1 2 3 4 5
%e A296620    1  . 1 1 1 1 . . . . . . . . . .
%e A296620    2  1 . 1 . . 1 1 . . . . . . . .
%e A296620    3  1 1 . . . . . 1 1 . . . . . .
%e A296620    4  1 . . . . . . . . 1 1 1 . . .
%e A296620    5  1 . . . . . . . . . . . 1 1 1
%e A296620    6  . 1 . . . . . . . 1 1 . 1 . .
%e A296620    7  . 1 . . . . . . . . . 1 . 1 1
%e A296620    8  . . 1 . . . . . . 1 . 1 . 1 .
%e A296620    9  . . 1 . . . . . . . 1 . 1 . 1
%e A296620   10  . . . 1 . 1 . 1 . . . . . . 1
%e A296620   11  . . . 1 . 1 . . 1 . . . . 1 .
%e A296620   12  . . . 1 . . 1 1 . . . . 1 . .
%e A296620   13  . . . . 1 1 . . 1 . . 1 . . .
%e A296620   14  . . . . 1 . 1 1 . . 1 . . . .
%e A296620   15  . . . . 1 . 1 . 1 1 . . . . .
%e A296620 .
%e A296620 Examples of unique graphs with maximum diameter:
%e A296620 Adjacency matrix of the graph of diameter 4 on 11 nodes:
%e A296620       1 2 3 4 5 6 7 8 9 0 1
%e A296620    1  . 1 1 1 1 . . . . . .
%e A296620    2  1 . 1 1 1 . . . . . .
%e A296620    3  1 1 . 1 1 . . . . . .
%e A296620    4  1 1 1 . . 1 . . . . .
%e A296620    5  1 1 1 . . 1 . . . . .
%e A296620    6  . . . 1 1 . 1 1 . . .
%e A296620    7  . . . . . 1 . . 1 1 1
%e A296620    8  . . . . . 1 . . 1 1 1
%e A296620    9  . . . . . . 1 1 . 1 1
%e A296620   10  . . . . . . 1 1 1 . 1
%e A296620   11  . . . . . . 1 1 1 1 .
%e A296620 .
%e A296620 Adjacency matrix of the graph of diameter 7 on 16 nodes:
%e A296620       1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6
%e A296620    1  . 1 1 1 1 . . . . . . . . . . .
%e A296620    2  1 . 1 1 1 . . . . . . . . . . .
%e A296620    3  1 1 . 1 1 . . . . . . . . . . .
%e A296620    4  1 1 1 . . 1 . . . . . . . . . .
%e A296620    5  1 1 1 . . 1 . . . . . . . . . .
%e A296620    6  . . . 1 1 . 1 1 . . . . . . . .
%e A296620    7  . . . . . 1 . 1 1 1 . . . . . .
%e A296620    8  . . . . . 1 1 . 1 1 . . . . . .
%e A296620    9  . . . . . . 1 1 . 1 1 . . . . .
%e A296620   10  . . . . . . 1 1 1 . 1 . . . . .
%e A296620   11  . . . . . . . . 1 1 . 1 1 . . .
%e A296620   12  . . . . . . . . . . 1 . . 1 1 1
%e A296620   13  . . . . . . . . . . 1 . . 1 1 1
%e A296620   14  . . . . . . . . . . . 1 1 . 1 1
%e A296620   15  . . . . . . . . . . . 1 1 1 . 1
%e A296620   16  . . . . . . . . . . . 1 1 1 1 .
%Y A296620 Cf. A006820 (row sums), A204329, A294733 (number of terms in each row for odd n), A296525 (number of terms in each row for even n).
%K A296620 nonn,tabf
%O A296620 5,5
%A A296620 _Hugo Pfoertner_, Dec 17 2017