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.

A296526 Number of connected k-regular graphs on 2*n nodes with maximal diameter D(n,k) A296525 written as array T(n,k), 2 <= k < 2*n.

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%I A296526 #22 Dec 21 2017 07:21:56
%S A296526 1,1,1,2,1,1,1,3,6,3,1,1,1,1,35,60,21,5,1,1,1,2,16,2391,7849,1547,94,
%T A296526 9,1,1,1,1,58,1,2757433,21609301,3459386,88193,540,13,1,1,1,4,1,154
%N A296526 Number of connected k-regular graphs on 2*n nodes with maximal diameter D(n,k) A296525 written as array T(n,k), 2 <= k < 2*n.
%D A296526 See A296525 for references and links.
%e A296526                                Degree r
%e A296526         2   3   4   5    6        7        8     9   10   11 12 13 14 15
%e A296526    n  ------------------------------------------------------------------
%e A296526    4 |  2   1  Diameter A296525
%e A296526      |  1   1  Number of graphs with this diameter (this sequence)
%e A296526      |
%e A296526    6 |  3   2   2   1
%e A296526      |  1   2   1   1
%e A296526      |
%e A296526    8 |  4   3   2   2    2        1
%e A296526      |  1   3   6   3    1        1
%e A296526      |
%e A296526   10 |  5   5   3   2    2        2       2      1
%e A296526      |  1   1  35  60   21        5       1      1
%e A296526      |
%e A296526   12 |  6   6   4   3    2        2       2      2    2    1
%e A296526      |  1   2  16 2391 7849     1547     94      9    1    1
%e A296526      |
%e A296526   14 |  7   8   5   5    3        2       2      2    2    2  2  1
%e A296526      |  1   1  58   1 2757433 21609301 3459386 88193 540  13  1  1
%e A296526      |                 lower bounds
%e A296526   16 |  8   9   7   5  >=4      >=3       2      2    2    2  2  2  2  1
%e A296526      |  1   4   1  154   ?        ?       ?      ?    ?    ?4207 21 1  1
%e A296526      |              lower bounds
%e A296526   18 |  9  11 >=8 >=6  >=4      >=4     >=3      2    2    2  2  2  2  2
%e A296526      |  1   1   ?   ?    ?        ?       ?      ?    ?    ?  ? ?42110 33
%e A296526 .
%e A296526 a(35)=1 corresponds to the only 5-regular graph on 14 nodes with diameter 5.
%e A296526 Its adjacency matrix is
%e A296526 .
%e A296526       1 2 3 4 5 6 7 8 9 0 1 2 3 4
%e A296526    1  . 1 1 1 1 1 . . . . . . . .
%e A296526    2  1 . 1 1 1 1 . . . . . . . .
%e A296526    3  1 1 . 1 1 . 1 . . . . . . .
%e A296526    4  1 1 1 . . 1 1 . . . . . . .
%e A296526    5  1 1 1 . . 1 1 . . . . . . .
%e A296526    6  1 1 . 1 1 . 1 . . . . . . .
%e A296526    7  . . 1 1 1 1 . 1 . . . . . .
%e A296526    8  . . . . . . 1 . 1 1 1 1 . .
%e A296526    9  . . . . . . . 1 . 1 1 . 1 1
%e A296526   10  . . . . . . . 1 1 . . 1 1 1
%e A296526   11  . . . . . . . 1 1 . . 1 1 1
%e A296526   12  . . . . . . . 1 . 1 1 . 1 1
%e A296526   13  . . . . . . . . 1 1 1 1 . 1
%e A296526   14  . . . . . . . . 1 1 1 1 1 .
%e A296526 .
%e A296526 A shortest walk along 5 edges is required to reach node 13 from node 1.
%e A296526 All others of the A068934(97)=3459383 5-regular graphs on 14 nodes have smaller diameters, i.e., 258474 with diameter 2, 3200871 with diameter 3, and 37 with diameter 4 (see A296621).
%Y A296526 Cf. A068934, A204329, A294733, A296524, A296525, A296621.
%K A296526 nonn,tabf,hard,more
%O A296526 2,4
%A A296526 _Hugo Pfoertner_, Dec 14 2017