The zig-zag chain as an extremal value of VDB topological indices of polyomino chains (2016)
We give conditions on the numbers under which a vertex-degree-based topological index T I of the form T I where G is a graph with n vertices and m is the number of ij-edges, has the zigzag chain as an extreme value among all polyomino chains. As a consequence, we deduce that over the polyomino chains, the zigzag chain has the maximal value of the Randić index, the sum-connectivity index, the harmonic index, and the geometric-arithmetic index, and the minimal value of the first Zagreb index, second Zagreb index, and atom-bond-connectivity index.