Guide to solving Harary's exercises Most of Harary's harder exercises are research problems (although solved), that need almost always a single key idea as a breakthrough. Often it so happens that even after thinking for a long time no solution comes to mind. 
I am a beginner in Graph Theory. How should I solve the problems from Harary? Often what I do is, I have no option other than looking up the original paper where the solution was published, get some idea on how to start, and then sometimes I am able to complete the proof.
For example, I am stuck for some time on this problem: 

If a graph has diameter $d$ and girth $2d+1$ then it is regular.

This also was a research problem solved. I think Harary should have given some hints on solving the harder problems.
What I know is, for any simple graph, if $D$ is the diameter, then the girth $\leq 2D+1$. But what happens when there is equality? I tried to start with vertices $u$ and $v$, with $deg(u)>deg(v)$ and whether $u$ is connected to the cycle, or $v$ is connected to $u$, etc. There are so many things at once!
Could someone please give me a hint only to start? I haven't seen the solution to this problem and have been trying it. However, I am convinced that the way problems have been solved, I could never have done them. All I would have spent are fruitless months. 

Choose vertices $a$ and $u$ at maximum distance. There is one neighbor of $a$ at distance $D-1$ from $u$. What is the distance from $u$ of the other neighbors? Working from here, that $a$ and $v$ have the same valency.
Now consider a cycle of length $2D+1$, and prove that all vertices on it have the same valency.
To be fair to Harary, this is a reasonable problem for a graduate course, although hard to get started on.
