A348461 -id:A348461 - cp's OEIS frontend

A348462 Size of largest bipartite biregular Moore graph of diameter 6 and degrees n and 2.

12, 35, 78, 147, 248

Offset: 2

N. J. A. Sloane, Oct 31 2021

a(7) >= 387, a(8) = 570, a(9) = 803, a(10) = 1092.

G. Araujo-Pardo, C. Dalfó, M. Á. Fiol and N. López, Bipartite biregular Moore graphs, arXiv:2103.11443 [math.CO], 2021.
G. Araujo-Pardo, C. Dalfó, M. Á. Fiol and N. López, Bipartite biregular Moore graphs, Discrete Math., 334 (2021), # 112582.

Empirical observation: For the terms a(2)-a(6) and a(8)-a(10) a(n) = A081437(n-1) + 2. It is unknown whether this is also valid for n = 7 and for n > 10. - Hugo Pfoertner, Oct 31 2021

a(n) <= A027620(n-2) + 3 = A081437(n-1) + 2 (the Moore bound). - Pontus von Brömssen, Oct 31 2021

A348463 Size of largest bipartite biregular Moore graph of diameter 6 and degrees n and n.

Original entry on oeis.org

12, 126, 728, 2730, 7812

Offset: 2

N. J. A. Sloane, Oct 31 2021

18660 <= a(7) <= 18662, a(8) = 39216, a(9) = 74898, a(10) = 132860.

Table 3 from these references gives the size of the largest bipartite biregular Moore graph of diameter 3 and degrees n and n, and appears to match 2*A002061.

G. Araujo-Pardo, C. Dalfó, M. Á. Fiol and N. López, Bipartite biregular Moore graphs, arXiv:2103.11443 [math.CO], 2021. See Table 2.
G. Araujo-Pardo, C. Dalfó, M. Á. Fiol and N. López, Bipartite biregular Moore graphs, Discrete Math., 334 (2021), # 112582. See Table 3.

Cf. A002061, A053700, A152031, A348461, A348462.

Empirical observation: a(n) = 2*(A152031(n-1) + 1) matches terms a(2)-a(6) and a(8)-a(10). - Hugo Pfoertner, Oct 31 2021

a(n) <= 2*A053700(n-1) = 2*(A152031(n-1) + 1) (the Moore bound). - Pontus von Brömssen, Oct 31 2021

cp's OEIS Frontend

A348462 Size of largest bipartite biregular Moore graph of diameter 6 and degrees n and 2.

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