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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 8-vertex graphs of maximal degree 2?
Jan
28
comment 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
revised Induced subgraphs of small strongly regular graphs
deleted 80 characters in body
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
comment 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).
Jan
28
comment Induced subgraphs of small strongly regular graphs
in my old papers I reconstructed subgraphs induced on the common neighbours of a pair of non-adjacent vertices. But it was always the case that I knew much more about $N(v)$ than here.
Jan
26
comment Irreducibility of a polynomial
oops, sorry, voted to reopen.
Jan
26
comment Can all unit-distance graphs have their vertices at algebraic integers?
@Ilya: ah, right. And not only into a 6-wheel, but any subgraph of the hexagonal lattice. I wonder if this is the complete answer.
Jan
26
comment Can all unit-distance graphs have their vertices at algebraic integers?
@Ilya: good point. This means that $G$'s with a homomorphisms to 6-cycle is a good class, in terms of the original question. (No idea why such graphs are interesting though) :-)
Jan
26
revised Largest eigenvalue adjacency matrix-link deletion
typo fixed
Jan
26
comment Can all unit-distance graphs have their vertices at algebraic integers?
How about adding a bit of intuition, say do you know such $f$ for the triangle? (and if yes, then one immediately has $f$ for the 3-colourable graphs).
Jan
26
revised Can every finite abelian $p$-group with duality pairing be written as cokernel of a symmetric matrix over the $p$-adic integers?
edited title
Jan
24
comment Can a graph be reconstructed from its cycle lengths?
It seems that if you know this sequence and the adjacency matrix of the graph, then you can compute the matching polynomial, which is #P-complete.
Jan
23
comment Open access journals in number theory
IMHO a publication of a close to final version on arxiv.org is good enough for all practical purposes.
Jan
23
comment accelerate convex optimization by proximal projection
can't you just stop your quadratic optimisations early?
Jan
23
comment research on the structure/properties of permutation matrix/table with $(i,j)th$ entry as $\pi_j\circ \pi_i^{-1}$
it's not clear what kind of order on permutations you are talking about, and, indeed, what the entries of these tables are.