Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 598517, 7 pages
http://dx.doi.org/10.1155/2013/598517
Research Article

The Atom-Bond Connectivity Index of Catacondensed Polyomino Graphs

Jinsong Chen,1,2 Jianping Liu,1 and Qiaoliang Li2

1College of Mathematics and Computer Science, Fuzhou University, Fuzhou, Fujian 350108, China
2College of Mathematics and Computer Science, Hunan Normal University, Changsha, Hunan 410081, China

Received 3 January 2013; Accepted 4 February 2013

Academic Editor: Zhengkun Huan

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.

Abstract

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.