On certain regular graphs of girth 5 (Q1066159)

Let f(v,g) be the number of vertices of a (v,g)-cage (regular graph of degree v and girth g with the least possible number of vertices). In the paper it is proved: Theorem. Let \(v\geq 7\) be an integer such that v-2 is a prime power. Then the following statements hold: (a) \(f(v,5)\leq 2(v- 2)^ 2\) (b) If n is an integer such that \(3\leq n\leq v\), then \(f(n,5)\leq 2(v-2)(n-2).\)