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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. 4
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, 9, 1, 1, 1, 1, 58, 1, 2757433, 21609301, 3459386, 88193, 540, 13, 1, 1, 1, 4, 1, 154 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,4

REFERENCES

See A296525 for references and links.

LINKS

Table of n, a(n) for n=2..47.

EXAMPLE

                               Degree r

        2   3   4   5    6        7        8     9   10   11 12 13 14 15

   n  ------------------------------------------------------------------

   4 |  2   1  Diameter A296525

     |  1   1  Number of graphs with this diameter (this sequence)

     |

   6 |  3   2   2   1

     |  1   2   1   1

     |

   8 |  4   3   2   2    2        1

     |  1   3   6   3    1        1

     |

  10 |  5   5   3   2    2        2       2      1

     |  1   1  35  60   21        5       1      1

     |

  12 |  6   6   4   3    2        2       2      2    2    1

     |  1   2  16 2391 7849     1547     94      9    1    1

     |

  14 |  7   8   5   5    3        2       2      2    2    2  2  1

     |  1   1  58   1 2757433 21609301 3459386 88193 540  13  1  1

     |                 lower bounds

  16 |  8   9   7   5  >=4      >=3       2      2    2    2  2  2  2  1

     |  1   4   1  154   ?        ?       ?      ?    ?    ?4207 21 1  1

     |              lower bounds

  18 |  9  11 >=8 >=6  >=4      >=4     >=3      2    2    2  2  2  2  2

     |  1   1   ?   ?    ?        ?       ?      ?    ?    ?  ? ?42110 33

.

a(35)=1 corresponds to the only 5-regular graph on 14 nodes with diameter 5.

Its adjacency matrix is

.

      1 2 3 4 5 6 7 8 9 0 1 2 3 4

   1  . 1 1 1 1 1 . . . . . . . .

   2  1 . 1 1 1 1 . . . . . . . .

   3  1 1 . 1 1 . 1 . . . . . . .

   4  1 1 1 . . 1 1 . . . . . . .

   5  1 1 1 . . 1 1 . . . . . . .

   6  1 1 . 1 1 . 1 . . . . . . .

   7  . . 1 1 1 1 . 1 . . . . . .

   8  . . . . . . 1 . 1 1 1 1 . .

   9  . . . . . . . 1 . 1 1 . 1 1

  10  . . . . . . . 1 1 . . 1 1 1

  11  . . . . . . . 1 1 . . 1 1 1

  12  . . . . . . . 1 . 1 1 . 1 1

  13  . . . . . . . . 1 1 1 1 . 1

  14  . . . . . . . . 1 1 1 1 1 .

.

A shortest walk along 5 edges is required to reach node 13 from node 1.

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).

CROSSREFS

Cf. A068934, A204329, A294733, A296524, A296525, A296621.

Sequence in context: A291709 A326323 A257493 * A259844 A112707 A196017

Adjacent sequences:  A296523 A296524 A296525 * A296527 A296528 A296529

KEYWORD

nonn,tabf,hard,more

AUTHOR

Hugo Pfoertner, Dec 14 2017

STATUS

approved

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Last modified January 23 19:12 EST 2020. Contains 331175 sequences. (Running on oeis4.)