1,795 reputation
923
bio website
location
age 26
visits member for 4 years, 1 month
seen 16 hours ago

If you have any good math exercises to share feel free to contribute them on http://exwiki.org


Jan
19
comment Can we say anything about the order of the second largest eigen-value?
You should then try to figure something out of the formula for the eigenvalues of a vt graph. Note that in general vertex transitive does not give you much of a difference. There are pairs of vertex transitive and not vertex transitive regular graphs with the same value of your expression.
Jan
11
comment Path cover in directed graphs
What it says is that on each of the paths of $\mathcal{P}$ you can pick a vertex so that the resulting vertices will be mutually non-adjacent.
Dec
7
comment Semi-hamiltonian graph.
@user180834 I wrote a complete solution.
Dec
7
comment Semi-hamiltonian graph.
@user180834 Can you answer the question in the hint?
Dec
7
comment Semi-hamiltonian graph.
What do you mean by semi-Hamiltonian?
Nov
29
comment Diameter of a Connected Graph
@sam_rox Yes, you are right. Thanks for the remark, I've corrected the page.
Nov
20
comment Determinant of the Kronecker product involving the identity
@Surb Err you're right I mean the Kronecker product!
Nov
20
comment orbits/canonical labelling of colored graphs
Hi! I am using Sage which AFAIK does not support this feature.
Nov
11
comment Number of words not having a subword of length k with only one letter
Thanks, that was very useful! Do you perhaps see a way to obtain an asymptotic estimate? I don't see a good way given that the poles of $f(z)$ are not directly known.
Nov
1
comment Determine a formula for the number of triangles in the line graph $L(G)$ in term of quantities in $G$
Just some pointers - every triangle in $G$ is also a triangle in $L(G).$ If $v$ i a vertex of degree $d$ then its edges give rise to $K_{d}$ in $L(G).$
Nov
1
comment Paper claiming a graph isomorphism that isn't actually an isomorphism?
@Zaaier What exactly do you want to implement? Just for isomorphism testing there are many free implementations online.
Oct
28
comment Upper bound for the number of hamilton cycles in a cubic graph
@Peter I forgot to mention that in this context $c$ can as well be infinity.
Oct
27
comment Upper bound for the number of hamilton cycles in a cubic graph
Exactly. What you do know though is that the limit you mention is $\leq c$ for some $c > 0.$
Oct
20
comment Proportion of asymmetric graphs
I believe you can figure this out from the book by Godsil and Royle (algebraic graph theory) see page 24.
Oct
17
comment how should I show that list chromatic number of $K_{3,3}=3$?
Perhaps this helps? exwiki.org/mw/…
Oct
2
comment $2$-connected graphs with a line graph containing no hamilton cycle
There you go then!
Oct
2
comment $2$-connected graphs with a line graph containing no hamilton cycle
@Peter Yes it is the least example.
Oct
2
comment $2$-connected graphs with a line graph containing no hamilton cycle
Hm.. what is surely true is that if $G$ is $2$-edge connected then $L(G)$ is $2$-connected. This may give a clue for counterexamples.
Oct
2
comment $2$-connected graphs with a line graph containing no hamilton cycle
Have you checked this paper sciencedirect.com/science/article/pii/S0893965912001036 dealing with a conjecture of Thomassen, stating that every $4$-connected line graph is hamiltonian? Its not really what you're asking for but it may offer some insight.
Sep
27
comment Length of longest cycle in this graph
I suggest you check the documentation related to the graph theory module sagemath.org/doc/reference/graphs/sage/graphs/graph.html