OFFSET
1,2
COMMENTS
The Sierpinski graph S_n has (3+3^n)/2 vertices and 3^n edges. The chromatic polynomial of S_n has (3+3^n)/2+1 coefficients.
LINKS
Alois P. Heinz, Rows n = 1..7, flattened
Eric Weisstein's World of Mathematics, Chromatic Polynomial.
Eric Weisstein's World of Mathematics, Sierpiński Gasket Graph.
Wikipedia, Chromatic Polynomial.
EXAMPLE
3 example graphs: o
. / \
. o---o
. / \ / \
. o o---o---o
. / \ / \ / \
. o o---o o---o o---o
. / \ / \ / \ / \ / \ / \ / \
. o---o o---o---o o---o---o---o---o
Graph: S_1 S_2 S_3
Vertices: 3 6 15
Edges: 3 9 27
The Sierpinski graph S_1 is equal to the cycle graph C_3 with chromatic polynomial q^3 -3*q^2 +2*q => [1, -3, 2, 0].
Triangle T(n,k) begins:
1, -3, 2, 0;
1, -9, 32, -56, 48, -16, ...
1, -27, 339, -2625, 14016, -54647, ...
1, -81, 3204, -82476, 1553454, -22823259, ...
1, -243, 29295, -2336013, 138604878, -6526886841, ...
1, -729, 265032, -64069056, 11585834028, -1671710903793, ...
1, -2187, 2389419, -1738877625, 948268049436, -413339609377179, ...
CROSSREFS
KEYWORD
AUTHOR
Alois P. Heinz, Jul 20 2011
STATUS
approved