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.

Showing 1-4 of 4 results.

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

Original entry on oeis.org

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, 2, 2, 2, 2, 2, 2, 1, 8, 9, 7, 5
Offset: 2

Views

Author

Hugo Pfoertner, Dec 14 2017

Keywords

Comments

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

Examples

			Table starts:
Degree = 2  3  4  5  6  7  8  9
n= 4 :   2  1
n= 6 :   3  2  2  1
n= 8 :   4  3  2  2  2  1
n=10 :   5  5  3  2  2  2  2  1
...
See example in A296526 for a complete illustration of the irregular table.

Links

Crossrefs

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

Extensions

a(46) corresponding to the quintic graph on 16 nodes from Hugo Pfoertner, Dec 19 2017

A294733 Maximal diameter of connected (2*k)-regular graphs on 2*n+1 nodes written as triangular array T(n,k), 1 <= k <= n.

Original entry on oeis.org

1, 2, 1, 3, 2, 1, 4, 2, 2, 1, 5, 4, 2, 2, 1, 6, 5, 2, 2, 2, 1, 7, 6, 4, 2, 2, 2, 1, 8
Offset: 1

Views

Author

Hugo Pfoertner, Dec 14 2017

Keywords

Comments

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

Examples

			Table starts:
Degree= 2   4   6   8  10  12  14  16
n= 3  : 1
n= 5  : 2   1
n= 7  : 3   2   1
n= 9  : 4   2   2   1
n=11  : 5   4   2   2   1
n=13  : 6   5   2   2   2   1
n=15  : 7   6   4   2   2   2   1
n=17  : 8 >=7 >=4   2   2   2   2   1

Links

Crossrefs

Cf. A068934, A294732, A296524, A296525, A296526.

A296524 Number of connected (2*k)-regular graphs on 2*n+1 nodes with maximal diameter D(n,k) A294733 written as triangular array T(n,k), 1 <= k <= n.

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 1, 16, 4, 1, 1, 1, 266, 6, 1, 1, 5, 367860, 10786, 10, 1, 1, 19, 1
Offset: 1

Views

Author

Hugo Pfoertner, Dec 14 2017

Keywords

Comments

The next term a(24) corresponding to the 6-regular graphs on 15 nodes is conjectured to be 1. It seems that there exists only one graph with diameter A294733(24)=4. Its adjacency matrix is
1 2 3 4 5 6 7 8 9 0 1 2 3 4 5
1 . 1 1 1 1 1 1 . . . . . . . .
2 1 . 1 1 1 1 1 . . . . . . . .
3 1 1 . 1 1 1 1 . . . . . . . .
4 1 1 1 . 1 1 1 . . . . . . . .
5 1 1 1 1 . 1 1 . . . . . . . .
6 1 1 1 1 1 . . 1 . . . . . . .
7 1 1 1 1 1 . . 1 . . . . . . .
8 . . . . . 1 1 . 1 1 1 1 . . .
9 . . . . . . . 1 . 1 1 . 1 1 1
10 . . . . . . . 1 1 . . 1 1 1 1
11 . . . . . . . 1 1 . . 1 1 1 1
12 . . . . . . . 1 . 1 1 . 1 1 1
13 . . . . . . . . 1 1 1 1 . 1 1
14 . . . . . . . . 1 1 1 1 1 . 1
15 . . . . . . . . 1 1 1 1 1 1 .
The distance of 4 is achieved between nodes 1 and 13. None of the remaining 1470293674 graphs seems to have a diameter > 3.
The conjecture is confirmed using Markus Meringer's GenReg program. Aside from the 1 shown 6-regular graph on 15 nodes with diameter 4 there are 870618932 graphs with diameter 2 and 599674742 graphs with diameter 3. - Hugo Pfoertner, Dec 19 2017

Examples

			                 Degree r
        2   4    6     8    10   12   14  16
   n  --------------------------------------
   3 |  1  Diameter A294733
     |  1  Number of graphs with this diameter (this sequence)
     |
   5 |  2   1
     |  1   1
     |
   7 |  3   2    1
     |  1   2    1
     |
   9 |  4   2    2     1
     |  1  16    4     1
     |
  11 |  5   4    2     2     1
     |  1   1   266    6     1
     |
  13 |  6   5    2     2     2    1
     |  1   5 367860 10786  10    1
     |
  15 |  7   6    4     2     2    2   1
     |  1  19    1     ?     ?   17   1
     |
  17 |  8   7  >=4     2     2    2   2    1
     |  1  33    ?     ?     ?    ?  25    1
.
a(12)=1 corresponds to the only 4-regular graph on 11 nodes with diameter 4.
Its adjacency matrix is
.
      1 2 3 4 5 6 7 8 9 0 1
   1  . 1 1 1 1 . . . . . .
   2  1 . 1 1 1 . . . . . .
   3  1 1 . 1 1 . . . . . .
   4  1 1 1 . . 1 . . . . .
   5  1 1 1 . . 1 . . . . .
   6  . . . 1 1 . 1 1 . . .
   7  . . . . . 1 . . 1 1 1
   8  . . . . . 1 . . 1 1 1
   9  . . . . . . 1 1 . 1 1
  10  . . . . . . 1 1 1 . 1
  11  . . . . . . 1 1 1 1 .
.
A shortest walk along 4 edges is required to reach node 9 from node 1.
All others of the A068934(60)=265 4-regular graphs on 11 nodes have smaller diameters, i.e., 37 with diameter 2 and 227 with diameter 3.

References

Links

  • M. Meringer, GenReg, Generation of regular graphs.

Crossrefs

Cf. A068934, A294733, A296525, A296526, A296620.

A296621 Number of 5-regular (quintic) connected graphs on 2*n nodes with diameter k written as irregular triangle T(n,k).

Original entry on oeis.org

1, 0, 3, 0, 60, 0, 5457, 2391, 0, 258474, 3200871, 37, 1, 0, 1041762, 2583730089, 364670, 154, 0
Offset: 3

Views

Author

Hugo Pfoertner, Dec 19 2017

Keywords

Comments

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

Examples

			Triangle begins:
                     Diameter
   n/ 1       2          3      4   5
   6: 0       1
   8: 0       3
  10: 0      60
  12: 0    5457       2391
  14: 0  258474    3200871     37   1
  16: 0 1041762 2583730089 364670 154
.
The adjacency matrix of the unique 5-regular graph on 14 nodes with diameter 5 is provided as example in A296526.

Links

Crossrefs

Cf. A006821 (row sums), A068934, A204329, A296525 (number of terms in each row), A296526, A296620.
Showing 1-4 of 4 results.

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