Publishing paper after graduation without advisor's name
This would depend entirely on whether he contributed to the work and, if so, how much. A minor contribution might require an acknowledgement, but if you worked together to develop the ideas in the paper he might well need to be co-author. You can probably judge this. 

However, there is another possible angle to consider. If you are planning to go on in academia and your old advisor can help you with that, then even a minor contribution leading to co-authorship might be good for you in the long run. That would be especially true if your advisor is a major figure in your field. 

But you have a delicate situation since the paper has already been accepted. Depending on what your advisor says you may want to delay, or you may want to use the acceptance to convince him that sole-authorship is fine. 



See this question to get information on predatory journals also: With Beall&#39;s List gone, how can I tell if a journal is spam?