A374311 - OEIS

%I #6 Feb 16 2025 08:34:07

%S 0,0,1,1,1,3,4,8,23,91,317,1353,6473,30834,148907,768178,3987517,

%T 20767030,110819167,599311836,3256610004

%N Number of planar graphs of order n with exactly one Hamiltonian cycle and girth at least 5.

%H Jan Goedgebeur, Barbara Meersman, and Carol T. Zamfirescu, <a href="https://arxiv.org/abs/1812.05650">Graphs with few Hamiltonian Cycles</a>, arXiv:1812.05650 [math.CO], 2018-2019. See Table 1 at p. 10.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PlanarGraph.html">Planar Graph</a>.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/UniquelyHamiltonianGraph.html">Uniquely Hamiltonian Graph</a>.

%Y Cf. A307957, A374310.

%K nonn,more,changed

%O 3,6

%A _Stefano Spezia_, Jul 04 2024