The Atom-Bond Connectivity Index of Catacondensed Polyomino Graphs

الملخص EN

Let G=(V,E) be a graph.

The atom-bond connectivity (ABC) index is defined as the sum of weights ((du+dv−2)/dudv)1/2 over all edges uv of G, where du denotes the degree of a vertex u of G.

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 h squares and determine the corresponding extremal graphs.