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Number of simple graphs on n nodes that are Euler (all nodes even) but not Eulerian (single cycle passes through all edges).
0

%I #6 Mar 30 2012 17:35:11

%S 0,0,0,0,0,1,2,7,20,76,334,2498,36398,1225629,89060804,12978995815,

%T 3646305137905,1947685504386516,1969840087225045340,

%U 3770491704215436784514,13674048211165798257589446,94122727377410134768239226418

%N Number of simple graphs on n nodes that are Euler (all nodes even) but not Eulerian (single cycle passes through all edges).

%C There are more Euler graphs than Eulerian graphs since there exist disconnected graphs having multiple disjoint cycles with each node even but for which no single cycle passes through all edges.

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

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

%F a(n) = A002854(n) - A133736(n).

%Y Cf. A002854, A133736.

%K nonn

%O 1,7

%A _Eric W. Weisstein_, Apr 26 2011