# Graphth

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## Registered User

 Name Graphth Member for 2 years Seen Mar 25 at 1:28 Website Location Age
 Dec13 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. Dec13 awarded ● Teacher Dec13 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. Dec13 answered What graph parameters are determined by parameters for strongly regular graph Dec13 asked What graph parameters are determined by parameters for strongly regular graph Dec12 revised Shannon capacity of all graphs of order 6added 4 characters in body Dec12 revised Shannon capacity of all graphs of order 6edited body Dec11 awarded ● Editor Dec11 revised Shannon capacity of all graphs of order 6added 64 characters in body; added 5 characters in body Dec11 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. Dec11 awarded ● Commentator Dec11 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 $\bar{G}$. Dec11 asked Shannon capacity of all graphs of order 6 Dec10 comment Lovasz theta function and independence number of product of simple odd-cyclesIsn't it still unknown whether $\Theta(C_{2k+1}) = \theta(C_{2k+1})$? Dec10 comment graphs with independence number = Shannon capacityBy 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 Dec10 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". Dec8 comment Non-isomorphic graphs of given order.You can use nauty inside of Sage. Dec8 comment graphs with independence number = Shannon capacitySo, have you ever answered any of your above questions? I am interested in all 3 separately. Dec8 asked Shannon capacity determined by $\alpha(G)$ and $\chi^*(\bar{G})$??? Dec2 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. Dec1 comment Upper bound on Shannon capacity based on independence numberTwo great answers, I am sorry I can not accept them both. Thanks for your help. Nov26 asked Upper bound on Shannon capacity based on independence number