Has the graph isomorphism problem been solved?
No.  That paper appears to be flawed.  The flaw was explained in a comment by Tracy Hall on MathOverflow.  A follow-up comment claims that the author later realized there is a flaw in his algorithm.

As Yuval explains, it is not uncommon to see attempts from amateurs to solve these problems; they tend to be flawed.  When it comes to results on famous open problems (e.g., P vs NP, graph isomorphism, etc.), I recommend looking to published literature in reputable peer-reviewed conferences and journals -- peer review is not perfect, but peer-reviewed papers have a much higher likelihood of being correct.