Graphth

185
Reputation
143 views
Is this your account?

Registered User 

Name Graphth
Member for 2 years
Seen Mar 25 at 1:28
Website
Location
Age
Dec
13
 comment What graph parameters are determined by parameters for strongly regular graph
@aaron The reason I used the complements of those graphs was because the chromatic numbers and independence numbers were equal for the graphs themselves, all of those being 4. But, I did check the girth for all 4 and the pairs with same parameters had equal girth.
Dec
13
 awarded ● Teacher
Dec
13
 comment What graph parameters are determined by parameters for strongly regular graph
@aaron Also equal. Sorry, I was in a hurry last night so I didn't have time to say everything I should have said.
Dec
13
 answered What graph parameters are determined by parameters for strongly regular graph
Dec
13
 asked What graph parameters are determined by parameters for strongly regular graph
Dec
12
 revised Shannon capacity of all graphs of order 6
added 4 characters in body
Dec
12
 revised Shannon capacity of all graphs of order 6
edited body
Dec
11
 awarded ● Editor
Dec
11
 revised Shannon capacity of all graphs of order 6
added 64 characters in body; added 5 characters in body
Dec
11
 comment Shannon capacity of all graphs of order 6
@gerry Yup, sorry about that. I had a typo in my definition of the Shannon capacity. Fixed it, thanks for your tip.
Dec
11
 awarded ● Commentator
Dec
11
 comment Shannon capacity of all graphs of order 6
@anthony $\alpha(G)$ is the independence number, the largest set of vertices such that none are adjacent to each other. $\chi(G)$ is the chromatic number of $G$, the least number of colors needed to color the vertices of $G$ such that no two adjacent vertices are colored the same. $\bar{G}$ is the complement of $G$, so that $v_i$ is adjacent to $v_j$ in $G$ if and only if $v_i$ is not adjacent to $v_j$ in $\bar{G}$.
Dec
11
 asked Shannon capacity of all graphs of order 6
Dec
10
 comment Lovasz theta function and independence number of product of simple odd-cycles
Isn't it still unknown whether $\Theta(C_{2k+1}) = \theta(C_{2k+1})$?
Dec
10
 comment graphs with independence number = Shannon capacity
By the way, did you know that if you do @Graphth before your response, then it will notify me of a response? I think since you wrote the question that it will notify you when I respond, even if I don't do @tobias
Dec
10
 comment graphs with independence number = Shannon capacity
$\alpha(G) = \Theta(G)$ does not imply $\alpha(G) = \vartheta(G)$. Haemers gives a counterexample in "An Upper Bound for the Shannon Capacity of a Graph".
Dec
8
 comment Non-isomorphic graphs of given order.
You can use nauty inside of Sage.
Dec
8
 comment graphs with independence number = Shannon capacity
So, have you ever answered any of your above questions? I am interested in all 3 separately.
Dec
8
 asked Shannon capacity determined by $\alpha(G)$ and $\chi^*(\bar{G})$???
Dec
2
 comment Writing papers in pre-LaTeX era?
At my grad school, there is a similar professor... but not in a good way. I guess he felt he was so good with ASCII characters that he just keeps using it, at least for his lecture notes. To write $x^2$, he writes $x$ on one line, and a 2 one line above and one space to the right.
Dec
1
 comment Upper bound on Shannon capacity based on independence number
Two great answers, I am sorry I can not accept them both. Thanks for your help.
Nov
26
 asked Upper bound on Shannon capacity based on independence number