A076435 -id:A076435 - cp's OEIS frontend

A088741 Number of connected strongly regular simple graphs on n nodes.

1, 1, 1, 2, 2, 3, 1, 3, 3, 5

Offset: 1

Eric W. Weisstein, Oct 12 2003

			1: K_1 (1 graph)
2: P_2 = K_2 (1 graph)
3: C_3 = K_3 (1 graph)
4: C_4, K_4 (2 graphs)
5: C_5, K_5 (2 graphs)
6: K_6, Ci_6(1,2), K_{3,3} (3 graphs)
Here, Ci_n(...) a circulant graph.

T. Hoppe and A. Petrone, Integer sequence discovery from small graphs, arXiv preprint arXiv:1408.3644 [math.CO], 2014.
T. Hoppe and A. Petrone, Integer sequence discovery from small graphs, Discr. Appl. Math. 201 (2016) 172-181.
Eric Weisstein's World of Mathematics, Strongly Regular Graph

Cf. A005177, A076435, A294405.

a(10) from the Encyclopedia of Finite Graphs (Travis Hoppe and Anna Petrone), Apr 11 2014

A076434 Number of weakly regular simple graphs on n nodes.

Original entry on oeis.org

0, 0, 0, 0, 0, 2, 4, 16, 21, 168, 544, 18992, 389451, 50314864

Offset: 1

Eric W. Weisstein, Oct 11 2002

Eric Weisstein's World of Mathematics, Weakly Regular Graph

Cf. A005176 (regular simple graphs on n nodes).
Cf. A294405 (connected weakly regular graphs on n nodes).
Cf. A076435 (strongly regular simple graphs on n nodes).

a(n) = A005176(n) - A076435(n). - Andrew Howroyd, Sep 03 2019

a(10) from Eric W. Weisstein, Oct 30 2017

a(11)-a(14) from Sean A. Irvine, Apr 04 2025

A051427 Number of strictly Deza graphs with n nodes.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 3, 2, 1, 0, 6, 1, 1, 1

Offset: 1

N. J. A. Sloane

From the Erikson et al. paper: We consider the following generalization of strongly regular graphs. A graph G is a Deza graph if it is regular and the number of common neighbors of two distinct vertices takes on one of two values (not necessarily depending on the adjacency of the two vertices). - Jonathan Vos Post, Jul 06 2008

M. Erickson, S. Fernando, W. H. Haemers, D. Hardy and J. Hemmeter, Deza graphs: A generalization of strongly regular graph, J. Combinatorial Designs, Vol 7, Issue 6, 395-405, Oct 21, 1999. See also here.
Sean A. Irvine, Java program (github)

Cf. A005176, A076434, A076435, A088741.

a(14)-a(15) from Sean A. Irvine, Sep 18 2021

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A088741 Number of connected strongly regular simple graphs on n nodes.

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A076434 Number of weakly regular simple graphs on n nodes.

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A051427 Number of strictly Deza graphs with n nodes.

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