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A129583
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Number of labeled bi-point-determining graphs with n vertices.
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5
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1, 1, 0, 0, 12, 312, 13824, 1147488, 178672128, 52666091712, 29715982846848, 32452221242518272, 69259424722321036032, 291060255757818125657088, 2421848956937579216663491584, 40050322614433939228627991906304, 1319551659023608317386779165849208832
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OFFSET
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0,5
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COMMENTS
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A bi-point determining graph is a graph in which no two vertices have the same neighborhoods or the same augmented neighborhoods (the augmented neighborhood of a vertex is the neighborhood of the vertex union the vertex itself).
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REFERENCES
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R. C. Read, The Enumeration of Mating-Type Graphs. Report CORR 89-38, Dept. Combinatorics and Optimization, Univ. Waterloo, 1989.
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LINKS
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FORMULA
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E.g.f.: G(2*log(1+x)-x) where G(x) is the e.g.f. of A006125.
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PROG
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(PARI) seq(n)={my(g=sum(k=0, n, 2^binomial(k, 2)*x^k/k!) + O(x*x^n)); Vec(serlaplace(subst(g, x, 2*log(1+x+O(x*x^n))-x)))} \\ _Andrew Howroyd_, May 06 2021
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CROSSREFS
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KEYWORD
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nice,nonn
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AUTHOR
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Ji Li (vieplivee(AT)hotmail.com), May 07 2007
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EXTENSIONS
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a(0)=1 prepended and terms a(13) and beyond from _Andrew Howroyd_, May 06 2021
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STATUS
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approved
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