A193130 - OEIS

A193130

Numbers of spanning trees of the cocktail party graphs.

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

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

Table of n, a(n) for n=1..13.

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

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

CROSSREFS

Cf. A091159 (up to isomorphism).

Sequence in context: A038015 A279525 A003753 * A006237 A181044 A339449

Adjacent sequences: A193127 A193128 A193129 * A193131 A193132 A193133

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein, Jul 16 2011

STATUS

approved