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10h

comment 
On Shannon Capacity of graph
so your last sentence in the question makes no sense. 
10h

comment 
On Shannon Capacity of graph
As I already said, $\lim_n\theta(G)^n=\infty$, (unless your graph has no edges), so it is not in $\mathbb{N}$. 
10h

revised 
On Shannon Capacity of graph
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10h

comment 
On Shannon Capacity of graph
There is Haemers bound on $\Theta(G)$ that is sometimes better than Lovazs's one, cf. en.wikipedia.org/wiki/Shannon_capacity_of_a_graph 
10h

comment 
On Shannon Capacity of graph
you should also talk about $\lim_n \theta(G^{...n})^{1/n}$. Indeed, $\theta(G)^n\to\infty$ as $n\to \infty$. 
10h

comment 
On Shannon Capacity of graph
you need $(\alpha())^{1/n}$ under the limit. 
2d

revised 
Induced subgraphs of small strongly regular graphs
rewritten from scratch 
Jan 29 
comment 
Induced subgraphs of small strongly regular graphs
7000 cases does not look as scary as 375000 cases, but still is not small. It depends of course on how big will be search trees when we extend... 
Jan 29 
comment 
Induced subgraphs of small strongly regular graphs
Do you really need to reconstruct the whole $N(v)$ in these cases? Or just enough vertices to get a subgraph with 19 eigenvalues not equal to 2? 
Jan 29 
comment 
Induced subgraphs of small strongly regular graphs
Did you check that each of these 7 graphs is a subgraph of one of the six 8vertex graphs from your list of possible subgraphs for $N(v)\cap N(w)$? Anyhow, one may try to extend the neighbourhood $N_v(w)$ of $w$ in $N(v)$ and reconstruct the missing edges between $N_v(w)$ and the other 14 vertices. If it gives you something without eigenvalue 2, you're done, as you get at least 19vertex subgraph this way. 
Jan 29 
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Induced subgraphs of small strongly regular graphs
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Jan 28 
comment 
Induced subgraphs of small strongly regular graphs
thus you are saying that 375219 can pruned quite a bit, right? Or it's 266 subgraphs of these 6 graphs on 8 vertices? 
Jan 28 
comment 
Induced subgraphs of small strongly regular graphs
I don't know if the condition that the neighbourhood of each vertex in each of these 375s219 subgraphs is a subgraph of one of these 6 graphs on 8 vertices is satisfied automatically, or you already checked it. But it's worth looking at, just in case. 
Jan 28 
comment 
Induced subgraphs of small strongly regular graphs
Is the number 266 simply the total number of 8vertex graphs of maximal degree 2? 
Jan 28 
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Induced subgraphs of small strongly regular graphs
So, how about $u\neq w\not\in N(u)$, but $w\in N(v)$? This is what you can extract from that 375219 examples... 
Jan 28 
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Induced subgraphs of small strongly regular graphs
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Jan 28 
answered  Induced subgraphs of small strongly regular graphs 
Jan 28 
comment 
Induced subgraphs of small strongly regular graphs
No, I meant just that  but how do these cases depend upon $u$ and $w$ being adjacent? 
Jan 28 
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Induced subgraphs of small strongly regular graphs
Can you use your candidates to enumerate possibilities for $N(v)\cap N(u)\cap N(w)$, for $u,w\in N(v)$ ? 
Jan 28 
comment 
Induced subgraphs of small strongly regular graphs
@Jernej : basically, it might be possible to reconstruct all the possibilities for $N(v)$ using your lists (provided they aren't very long...). And this would be almost it (again, depending upon how long the resulting list is). 