Majorants and minorants in the graph class with given number of vertices and diameter

Majorants (minorants), i.e., extremal graphs such that for any $i\ge0$ exact upper (lower) estimates for the number of different balls of the radius $i$ are attained at, are studied in the class of the $n$-vertex graphs with diameter $d$. For all parameters $n$ and $d$, the minorants are described explicitly. It is found out when the majorants exist in the class of $n$-vertex graphs with diameter $d$, and the corresponding extremal graphs are described. Il. 9, bibliogr. 8.