A class of additive multiplicative graph functions

Abstract

AbstractFor a fixed graph G, the capacity function for G, PG, is defined by PG(H) = limn→∞[γG(Hn)]1/n, where γG(H) is the maximum number of disjoint G's in H. In [2], Hsu proved that PK2 is multiplicative or not. In this paper, we prove that PG is multiplicative and additive for some graphs G which include K2. Some properties of PG are also discussed in this paper