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visits member for 2 years, 4 months
seen Oct 3 at 1:04

Oct
2
comment Is there a relationship between the clique of a graph and colouring of a graph?
May be you can give the example you have in mind about triangle free graph with arbitrarily large chromatic number.
Sep
30
comment Is there a relationship between the clique of a graph and colouring of a graph?
Thanks! Can you kindly explain the intuition behind behind being triangle free?
Sep
30
asked Is there a relationship between the clique of a graph and colouring of a graph?
Sep
27
comment A question about similarity transformation.
I want to disallow anything that would obviously lead to isomorphic graphs. I believe such an orbit does exist inside the group of transformations which would most often not lead to isomorphic graphs but would keep producing an infinite family of such graphs. I would think of it as 2 possible separate question (1) find a curve c(t) : [0,1] -> O(n) such that c(t)Ac(t)^{-1} is almost always some non-isomorphic d-regular adjacency matrix OR (2) find a B in O(n) such that B^kA(B^-1)^k is almost always some non-isomorphic d-regular adjacency matrix. I don't know which way of thinking is easier!
Sep
27
comment A question about similarity transformation.
@ChrisGodsil Yes I am thinking of cospectral regular graphs! :D I guess I should have said that I want non-trivial similarity transformations!
Sep
27
asked A question about similarity transformation.
Sep
22
comment Solving (for asymptotics) of certain recurrence equations.
So did you just guess this out of thin air?
Sep
21
comment Solving (for asymptotics) of certain recurrence equations.
The question is how do you guess that correct answer? I am quite certain that if you tweaked the coefficient of even of of the "T"s on the right then this guess would not have worked. Is there is a method?
Sep
21
asked Solving (for asymptotics) of certain recurrence equations.
Aug
29
comment Random walks on connected finite graphs
There is a path of length at most $n-1$.
Aug
29
comment Random walks on connected finite graphs
I was curious if there is a way to argue this using the idea of the Markov matrix $M$ where $M_{ij}$ is the probability of transition of the walker from vertex $j$ to $i$ i.e $1/deg(j)$. Then given an initial vertex $a$ and a final vertex $b$ and $n$, we have that $(M^n)_{ab}$ is the probability for the walker to go from $b$ to $a$ in $n$ steps. Now can one show that for $n\rightarrow \infty$ this matrix element tends to $1$?
Aug
29
comment Random walks on connected finite graphs
Can you kindly explain this idea of "diameter"?
Aug
29
comment Random walks on connected finite graphs
@user133281 Yes - that can be one meaning. Or one can also say that if one is given two specific vertices say $a$ and $b$ then with probability $1$ the random walker will reach $b$ from $a$ if allowed infinite steps.
Aug
29
asked Random walks on connected finite graphs
Aug
22
comment About putting $n$ distinct balls into $n$ distinct boxes.
And to make "k" the minimum filled label, why do you need exactly the first (k-1) boxes to be empty? One could have a situation where all the balls are in the k^th box and then the minimum label is still "k".
Aug
22
comment About putting $n$ distinct balls into $n$ distinct boxes.
When you write that expression, $^nC_1 \frac{(n-1)^{(n-1)} }{n^n}$ aren't you allowing for there to be multiple boxes with a single ball? Then the events you have summed over in calculating $E(M)$ are not disjoint - right?
Aug
22
revised About putting $n$ distinct balls into $n$ distinct boxes.
added 44 characters in body
Aug
22
comment About putting $n$ distinct balls into $n$ distinct boxes.
@DPoole The minimum value of the label among the boxes which are non-empty.
Aug
22
comment About putting $n$ distinct balls into $n$ distinct boxes.
@deinst Can you kindly write in details? If you could state the exact answers you have then I can match them for a start.
Aug
22
asked About putting $n$ distinct balls into $n$ distinct boxes.