  In a recursive way and by including a parameter, we introduce a family of
deterministic scale-free networks. The resulting networks exhibit small-world
effects. We calculate the exact results for the degree exponent, the clustering
coefficient and the diameter. The major points of our results indicate: the
degree exponent can be adjusted; the clustering coefficient of each individual
vertex is inversely proportional to its degree and the average clustering
coefficient of all vertices approaches to a nonzero value in the infinite
network order; and the diameter grows logarithmically with the number of
network vertices.
