How important is the choice of a guide/adviser for pursuing PhD in a topic I am really in a fix in my career.

I completed my Masters in 2014. I qualified in a PhD Scholarships Test in 2015 and in the same year joined in a University for research work.

My interest lies in Linear Algebra, Topology, Abstract Algebra. My guide offered  me to work in Spectral Graph Theory. As  I was not quite acquainted with the topic I took up this topic for research.

As I am reading on my own, I am getting stuck on many theorems and some problems.

My guide has said recently that he does not have much expertise on this topic  besides the preliminaries and hence he can't answer each and every problem of mine. He has said that the topic is new to him also. I have found now that also does not have any research papers to his name on Spectral Graph Theory as well. I was not aware of this before

My question is how important is the choice of a guide/adviser for pursuing PhD in a topic and what needs to be checked before joining him.

Is it wise  continuing to  work with him or should I look for some alternatives. Does getting a PhD depend a lot on your guide or I am  expecting a lot from my guide? Does pursuing a PhD mean you have to do all along yourself?

I know there are many in this site who have got a PhD or have served as guides/advisors for many students. Please help. Any suggestions will be helpful. I would be happy to give more inputs if required.
Working on a PhD in an area where your advisor appears to have little to no expertise in is fraught with danger. A PhD degree is in some sense an apprenticeship - while you need to do the heavy lifting, you also get/need to learn the tricks of the trade from an accomplished master. Every craft has subtler/finer aspects that are not acquired easily. Would you want to rely on someone who himself doesn't appear to know much, even at a high level? I wouldn't do a PhD with such an advisor for the same reasons I wouldn't learn painting from someone who doesn't know it himself/herself. 

On a more important side note, it might not be very wise to jump into a doctorate in an area you have such little knowledge/interest in. You do appear to have the right background, but even with that, doctoral level research in Spectral Graph Theory (and applications, if you are interested in them) is not going to be easy to pick up, even with an expert advisor.