T(G; x; y) is multiplicative over blocks; that is, if G has blocks B1,
. . . ,Bb, then
T(G; x; y) =
b
pi T(Bi, x, y)
i=1
These are a few examples that I could come up with:
G
1. nK1 = ¹Kn where 'K is the complement of K
2. Any tree
3. m loops
4. Cm
5. m jj edges
T(G, x, y)
1. 1
2. x^m
3. y^m
4. y+x+x^2+. . .+x^(m-1)
5. x+y+y^2+. . .+y^(m-1)
The actual problem would be nice.
If you're replying to a previous post, you should quote it. If you're
using Google Groups, don't click on the Reply link at the bottom of the
post; click on the More Options link at the top, then click on "Reply"
in the "menu" that pops up. The message will be posted.
Now: If you're asking how the Tutte Polynomial behaves with respect to
blocks, use the definition, assume you have a cut-vertex v in your
graph G, and go from there.
--- Christopher Heckman