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A296620
Number of 4-regular (quartic) connected graphs on n nodes with diameter k written as irregular triangle T(n,k).
2
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, 0, 1, 84103, 4006, 58, 0, 1, 722252, 82726, 493, 19, 0, 0, 6383913, 1647078, 6224, 202, 1, 0, 0, 55831405, 30291536, 96504, 2156, 33
OFFSET
5,5
COMMENTS
The results were found by applying the Floyd-Warshall algorithm to the output of Markus Meringer's GenReg program.
LINKS
M. Meringer, GenReg, Generation of regular graphs.
EXAMPLE
Triangle begins:
Diameter
n/ 1 2 3 4 5 6 7
5: 1
6: 0 1
7: 0 2
8: 0 6
9: 0 16
10: 0 24 35
11: 0 37 227 1x
12: 0 26 1502 16
13: 0 10 10561 202 5
14: 0 1x 84103 4006 58
15: 0 1x 722252 82726 493 19
16: 0 0 6383913 1647078 6224 202 1x
17: 0 0 55831405 30291536 96504 2156 33
.
x indicates provision of adjacency information below.
Examples of unique 4-regular graphs with minimum diameter:
Adjacency matrix of the graph of diameter 2 on 14 nodes:
1 2 3 4 5 6 7 8 9 0 1 2 3 4
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 .
12 . . . . 1 1 . . . 1 1 . . .
13 . . . . 1 . 1 . 1 . 1 . . .
14 . . . . 1 . . 1 1 1 . . . .
.
Adjacency matrix of the graph of diameter 2 on 15 nodes:
1 2 3 4 5 6 7 8 9 0 1 2 3 4 5
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 .
12 . . . 1 . . 1 1 . . . . 1 . .
13 . . . . 1 1 . . 1 . . 1 . . .
14 . . . . 1 . 1 1 . . 1 . . . .
15 . . . . 1 . 1 . 1 1 . . . . .
.
Examples of unique graphs with maximum diameter:
Adjacency matrix of the graph of diameter 4 on 11 nodes:
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 .
.
Adjacency matrix of the graph of diameter 7 on 16 nodes:
1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6
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 . . .
12 . . . . . . . . . . 1 . . 1 1 1
13 . . . . . . . . . . 1 . . 1 1 1
14 . . . . . . . . . . . 1 1 . 1 1
15 . . . . . . . . . . . 1 1 1 . 1
16 . . . . . . . . . . . 1 1 1 1 .
CROSSREFS
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).
Sequence in context: A293935 A285479 A327369 * A263789 A081153 A369278
KEYWORD
nonn,tabf
AUTHOR
Hugo Pfoertner, Dec 17 2017
STATUS
approved