How can we improve the following sentence?
Let $G$ be a planar graph with $n$ vertices with minimum degree $5$ with diameter two where $n$ is odd.
Firstly, I realized that I used "with" three in a row, so I made a modification by changing one of them to "of".
Let $G$ be a planar graph with $n$ vertices of minimum degree $5$ with diameter two where $n$ is odd.
However, I still believe that there's room for improvement such as the sentence is too long and feels quite cumbersome.
It often helps to break up sentences. Also, in this particular case, the sentence is ambiguous because you've separated the definition of $n$ from a qualification about $n$. Are you saying that $G$ has an odd number of vertices and all of them have degree at least $5$? Or are you saying that $G$ can have any number of vertices but that an odd number of them have degree at least $5$?
Assuming the former meaning is intended, I'd write it like this:
Let $G$ be a planar graph with an odd number of vertices, $n$, and diameter $2$. Assume each vertex has degree at least $5$.
If the latter meaning is intended, I'd write it like this:
Let $G$ be a planar graph of diameter $2$. Assume that an odd number, $n$, of the vertices of $G$ have degree at least $5$.