Copyright © 2013 Jinsong Chen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Let be a graph. The atom-bond connectivity (ABC) index is defined as the sum of weights over all edges of , where denotes the degree of a vertex of . In this paper, we give the atom-bond connectivity index of the zigzag chain polyomino graphs. Meanwhile, we obtain the sharp upper bound
on the atom-bond connectivity index of catacondensed polyomino graphs with squares and determine the corresponding extremal graphs.