Abstract
We demonstrate a usefulness of the notion of a connected graph for obtaining some common fixed point theorems. In particular, we establish two theorems of this type involving one, two and four sequences of maps. This generalizes among others the recent results of S. Chang [1], J. Jachymski [2], S. Sessa, R. N. Mukherjee and T. Som [3], and T. Taniguchi [4].