A193130 Numbers of spanning trees of the cocktail party graphs.

0, 4, 384, 82944, 32768000, 20736000000, 19271206305792, 24759631762948096, 42071440246337175552, 91403961001574400000000, 247248735803801600000000000, 815050629127324260701847945216, 3217014140995401936351315753959424

Offset: 1

Author

Eric W. Weisstein, Jul 16 2011

Keywords

• nonn
• easy

Comments

Number of trees on 2n labeled vertices containing no edges from a prescribed perfect matching. - Joel B. Lewis, Jun 20 2013

References

• Dragoš M. Cvetković, Michael Doob, Horst Sachs, Spectra of Graphs: Theory and Application, Academic Press, 1980.

Links

• Takashi Horiyama, Masahiro Miyasaka, Riku Sasaki, Isomorphism Elimination by Zero-Suppressed Binary Decision Diagrams, 30th Canadian Conference on Computational Geometry, 2018. See Table 2.
• Eric Weisstein's World of Mathematics, Cocktail Party Graph
• Eric Weisstein's World of Mathematics, Spanning Tree

Crossrefs

Cf. A091159 (up to isomorphism).

Formula

a(n) = n^(n-2) * (n-1)^n * 4^(n-1). [See "Spectra of graphs", p. 217; also observed by Joel B. Lewis, Jun 20 2013] - Andrey Zabolotskiy, Mar 18 2021