|
|
A338110
|
|
Number of spanning trees in the join of the disjoint union of two complete graphs each on n vertices with the empty graph on n vertices.
|
|
0
|
|
|
1, 128, 139968, 536870912, 5000000000000, 92442129447518208, 2988151979474457198592, 154742504910672534362390528, 12044329605471552321957641846784, 1342177280000000000000000000000000000, 206097683218942123873399068932507659403264, 42281678783395138381516145098915043145456549888
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
Equivalently, the graph can be described as the graph on 3*n vertices with labels 0..3*n-1 and with i and j adjacent iff A011655(i + j) = 1.
These graphs are cographs.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = n*(2*n)^(3*(n - 1)).
|
|
EXAMPLE
|
The adjacency matrix of the graph associated with n = 2 is: (compare A204437)
[0, 1, 1, 0, 1, 1]
[1, 0, 0, 1, 1, 0]
[1, 0, 0, 1, 0, 1]
[0, 1, 1, 0, 1, 1]
[1, 1, 0, 1, 0, 0]
[1, 0, 1, 1, 0, 0]
a(2) = 128 because the graph has 128 spanning trees.
|
|
MATHEMATICA
|
Table[n (2 n)^(3 (n - 1)), {n, 1, 10}]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|