The power graph P(G) of a finite group G is the graph whose
vertex set is G, and two elements in G are adjacent if one of them is a
power of the other. The purpose of this paper is twofold. First, we find the
complexity of a clique--replaced graph and study some applications. Second, we
derive some explicit formulas concerning the complexity
κ(P(G)) for various groups G such as the cyclic group of
order n, the simple groups L2(q), the extra--special p--groups of order
p3, the Frobenius groups, etc.Comment: 14 page