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Number of connected graphs on n vertices whose spectrum has n distinct eigenvalues.
1

%I #16 Mar 26 2015 07:20:47

%S 1,1,1,3,11,54,539,7319,209471,10000304

%N Number of connected graphs on n vertices whose spectrum has n distinct eigenvalues.

%C The spectrum refers to the eigenvalues of the adjacency matrix.

%H Travis Hoppe and Anna Petrone, <a href="https://github.com/thoppe/Encyclopedia-of-Finite-Graphs">Encyclopedia of Finite Graphs</a>

%H T. Hoppe and A. Petrone, <a href="http://arxiv.org/abs/1408.3644">Integer sequence discovery from small graphs</a>, arXiv preprint arXiv:1408.3644, 2014

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

%Y Cf. A064731 (integral graphs), A242953 (non-distinct spectrum graphs).

%K nonn,more

%O 1,4

%A _Travis Hoppe_ and _Anna Petrone_, May 27 2014

%E Corrected, original description as the "real spectrum" was incorrect, by _Travis Hoppe_, Mar 23 2015