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Number of connected chordal bipartite graphs on n unlabeled vertices.
2

%I #8 Apr 10 2024 09:34:21

%S 1,1,1,3,5,16,41,154,560,2550,12404,69536,428698,2947229,22288540,

%T 185226859,1682006569,16635022967,178525323313

%N Number of connected chordal bipartite graphs on n unlabeled vertices.

%C A chordal bipartite graph is a bipartite graph with no induced cycles longer than 4-cycles. Note that this is not the same as a bipartite graph which is chordal, as that would exclude all cycles.

%H Brendan McKay, <a href="https://users.cecs.anu.edu.au/~bdm/nauty/">nauty software </a> that can generate these graphs.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Chordal_bipartite_graph">Chordal bipartite graph</a>.

%e The 3 examples for n=4 are the 4-cycle, the star, and the path.

%Y Cf. A371867, A371869.

%K nonn,hard,more

%O 1,4

%A _Brendan McKay_, Apr 09 2024