The Atom-Bond Connectivity Index of Catacondensed Polyomino Graphs

Abstract

The Atom-Bond Connectivity Index of Catacondensed Polyomino Graphs: 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.