Nov
17 |
asked | Connection between the Chebyshev polynomials and the Faber polynomials |
Nov
1 |
comment |
Cycling through the Zeta Garden: Zeta functions for graphs, cycle index polynomials, and determinants
Interesting. Do you have something where I can read on this? |
Aug
17 |
revised |
Connection between Barnette conjecture and hardness of cubic graph decomposition
corrected some typos |
Aug
17 |
suggested | approved edit on Connection between Barnette conjecture and hardness of cubic graph decomposition |
May
24 |
revised |
An Expression for $\log\zeta(ns)$ derived from the Limit of the truncated Prime $\zeta$ Function
added 31 characters in body |
May
21 |
comment |
Cycling through the Zeta Garden: Zeta functions for graphs, cycle index polynomials, and determinants
Sorry for my narrow focus. Maybe the naming of the matrices kinda confused me... |
May
19 |
awarded | Excavator |
May
19 |
revised |
Cycling through the Zeta Garden: Zeta functions for graphs, cycle index polynomials, and determinants
added \operatorname |
May
19 |
revised |
Cycling through the Zeta Garden: Zeta functions for graphs, cycle index polynomials, and determinants
added \operatorname |
May
19 |
suggested | approved edit on Cycling through the Zeta Garden: Zeta functions for graphs, cycle index polynomials, and determinants |
May
19 |
suggested | approved edit on Cycling through the Zeta Garden: Zeta functions for graphs, cycle index polynomials, and determinants |
May
19 |
comment |
Cycling through the Zeta Garden: Zeta functions for graphs, cycle index polynomials, and determinants
I see. But shouldn't then bettter write $N_m = tr[(W_1)_n^m]$ like in Terras' paper? |
May
18 |
comment |
Cycling through the Zeta Garden: Zeta functions for graphs, cycle index polynomials, and determinants
Is this why your "Ihara" zeta function deals with backtracking (resp. powers of $A$) and neither mine nor M. Horton's Definition (Def. 2.7.: The closed path counting function $N_m$ is the number of closed paths $C$ of length $m$ in $G$ without backtracking or tails.) does? I think that it's related to Chebychev polynomials... |
May
18 |
awarded | Commentator |
May
18 |
comment |
Cycling through the Zeta Garden: Zeta functions for graphs, cycle index polynomials, and determinants
Hi again. Why do you say $\operatorname{det}(I-tA_n)$ and not $ \zeta_G(u) = \frac{(1-t^2)^{\chi(G)-1}}{\det(I - At + (k-1)t^2I)} $ like in Wiki:Ihara $\zeta$ function? Forgetting the inverse for the moment... |
Apr
30 |
comment |
cospectral graphs
The Google search just returns your question to me... |
Sep
24 |
awarded | Autobiographer |
Sep
10 |
comment |
Asymptotic density of k-almost primes
@TheMaskedAvenger or martin: could you post a link to the ArXiv paper? |
May
9 |
comment |
Ihara zeta and chromatic number of graphs
Dear Chris, when the IZF for regular graphs is defined via the spectrum of the adjacency matrix, how could this help to get IZF from Chebycheff Polynomials? |
May
9 |
comment |
Cycling through the Zeta Garden: Zeta functions for graphs, cycle index polynomials, and determinants
Tom, I'm confused. I thought the $N_m$ are closed loops without back tracking. But your formula the calculate it just uses powers of $A_n$ which includes backtracking. I got a nice answer by Chris Godsil, that shows a way to get returning paths without backtracking. It is linked to the question I referenced above... |