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%I #28 Jun 11 2019 05:36:29
%S 1,2,6,14,84,286,7266,63191
%N Number of simple graphs on n vertices with bandwidth equal to diameter-based lower bound.
%C Number of graphs for which the inequality bw(G) >= ceiling((n-1)/diameter(G)) holds with equality.
%C Equality holds for all nontrivial simple connected graphs on <= 4 nodes, so a(n) = A001349(n) for n = 2, 3, 4.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GraphBandwidth.html">Graph Bandwidth</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GraphDiameter.html">Graph Diameter</a>
%e 14 of the 21 graphs on 5 nodes satisfy the inequality with equality, the exceptions being K_2,3, K_1,1,3, K_1,1,1,2, W_5, the house X graph, the (4,1)-lollipop graph, and one other.
%K nonn,more
%O 2,2
%A _Eric W. Weisstein_, Jun 11 2019