|
%I #18 Jun 26 2024 18:12:26
%S 1,3,3,10,12,35,58,160,341,958,2444,7242,21190,67217,217335,740542,
%T 2593802,9444080,35383843
%N Number n-cyclic graphs.
%C Take the graph of an n-cycle and consider all possible contractions (including no contraction at all) that do not produce self-loops. Then eliminate multiple edges and count the nonisomorphic graphs.
%C n-cyclic graphs are distinct simple graphs on which there exists a closed n-walk.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GraphCycle.html">Graph Cycle</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/k-CyclicGraph.html">k-Cyclic Graph</a>
%H FlowProblem. <a href="https://web.archive.org/web/20161015202205/http://flowproblem.ru/cycles/explicit-formulae/ck-graphs">C_k-graphs</a>
%e a(4)=3 because the square loop gives itself and can be folded to give the tree on three vertices and the connected graph on two vertices:
%e ._.
%e |_| --> |_| + \/ + |
%K nonn,nice,more,hard
%O 3,2
%A Timothy K. Callahan (timcall(AT)math.la.asu.edu), Apr 10 2003
%E More terms from _Eric W. Weisstein_, Jan 08 2014
%E a(18)-a(21) from _Bert Dobbelaere_, Jun 26 2024
| 