The atom-bond connectivity index of catacondensed polyomino graphs
Summary: Let \(G = (V, E)\) be a graph. The atom-bond connectivity (ABC) index is defined as the sum of weights \(((d_u + d_v - 2)/d_ud_v)^{1/2}\) over all edges \(uv\) of \(G\), where \(d_u\) 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.
scientific article; zbMATH DE number 6175096