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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 (list; graph; refs; listen; history; text; internal format)
 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. Wikipedia, Distance (graph theory). Wikipedia, Floyd-Warshall algorithm. 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 A126869 Adjacent sequences:  A296617 A296618 A296619 * A296621 A296622 A296623 KEYWORD nonn,tabf AUTHOR Hugo Pfoertner, Dec 17 2017 STATUS approved

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Last modified July 28 00:54 EDT 2021. Contains 346316 sequences. (Running on oeis4.)