OFFSET
3,1
COMMENTS
The graph join is the graph obtained by adding all possible edges between different graphs to the graph union.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 3..80
Eric Weisstein's World of Mathematics, Spanning Tree
MAPLE
with(LinearAlgebra):
a:= proc(n) local h, i, M;
M:= Matrix(2*n, shape=symmetric);
for h in [seq(seq([i, j+n], j=1..n), i=1..n),
seq([[i, 1+(i mod n)], [n+i, n+1+(i mod n)]][], i=1..n)]
do M[h[]]:= -1 od;
for i to 2*n do M[i, i]:= -add(M[i, j], j=1..2*n) od;
Determinant(DeleteColumn(DeleteRow(M, 1), 1))
end:
seq(a(n), n=3..20); # Alois P. Heinz, Jul 17 2011
MATHEMATICA
a[n_] := Module[{h, i, M}, M = Array[0&, {2n, 2n}]; Do[M[[Sequence@@h]] = M[[Sequence@@Reverse[h]]] = -1, {h, Flatten[Table[{i, j+n}, {i, 1, n}, {j, 1, n}], 1] ~Join~ Flatten[Table[{{i, 1+Mod[i, n]}, {n+i, n+1 + Mod[i, n]}}, {i, 1, n}], 1]}]; For[i = 1, i <= 2n, i++, M[[i, i]] = -Sum[M[[i, j]], {j, 1, 2n}]]; Det[Rest /@ Rest[M]]];
Table[a[n], {n, 3, 20}] (* Jean-François Alcover, Feb 12 2023, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Jul 16 2011
EXTENSIONS
Description corrected by Eric W. Weisstein, May 10 2017
STATUS
approved