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Number of maximal independent vertex sets (and minimal vertex covers) in the n-odd graph.
1

%I #12 Jan 12 2024 01:05:33

%S 1,3,15,6127

%N Number of maximal independent vertex sets (and minimal vertex covers) in the n-odd graph.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MaximalIndependentVertexSet.html">Maximal Independent Vertex Set</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MinimalVertexCover.html">Minimal Vertex Cover</a>.

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

%o (Python)

%o from itertools import combinations

%o from networkx import empty_graph, find_cliques

%o def A290610(n):

%o G = empty_graph(combinations(range((n<<1)-1),n-1))

%o G.add_edges_from((a,b) for a, b in combinations(G,2) if not set(a).isdisjoint(b))

%o return sum(1 for c in find_cliques(G)) # _Chai Wah Wu_, Jan 11 2024

%K nonn,more

%O 1,2

%A _Eric W. Weisstein_, Aug 07 2017