A243332 Number of simple connected graphs with n nodes that are integral and triangle-free.

1, 1, 0, 1, 1, 3, 1, 3, 0, 14, 8, 18, 33, 75

Offset: 1

Author

Travis Hoppe and Anna Petrone, Jun 03 2014

Keywords

• nonn
• more

Links

• Travis Hoppe and Anna Petrone, Encyclopedia of Finite Graphs.
• Travis Hoppe and Anna Petrone, Integer sequence discovery from small graphs, arXiv:1408.3644 [math.CO], 2014.

Crossrefs

Cf. A064731 (integral graphs), A024607 (triangle-free graphs).

Programs

Sage

a243332 = lambda n: sum(1 for g in graphs.nauty_geng(f'-c -t {n}') if sum(m for ,m in g.charpoly().roots(ZZ))==n) # _Max Alekseyev, Jan 31 2024

Extensions

a(11)-a(14) from Max Alekseyev, Feb 02 2024