A189771 Number of simple graphs on n nodes that are Euler (all nodes even) but not Eulerian (single cycle passes through all edges).

0, 0, 0, 0, 0, 1, 2, 7, 20, 76, 334, 2498, 36398, 1225629, 89060804, 12978995815, 3646305137905, 1947685504386516, 1969840087225045340, 3770491704215436784514, 13674048211165798257589446, 94122727377410134768239226418

Offset: 1

Author

Eric W. Weisstein, Apr 26 2011

Keywords

• nonn

Comments

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.

Links

• Eric Weisstein's World of Mathematics, Euler Graph
• Eric Weisstein's World of Mathematics, Eulerian Graph

Crossrefs

Cf. A002854, A133736.

Formula

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