The linear chain as an extremal value of VDB topological indices of polyomino chains

Abstract

ABSTRACT: We give conditions on the numbers {ϕij} under which a vertex degree-based topological index T I of the form T I (G) = X 1≤i≤j≤n−1 mijϕij , where G is a graph with n vertices and mij is the number of ij-edges, has the linear chain as an extreme value among all polyomino chains. As a consequence, we deduce that over the polyomino chains, the linear chain has the maximal value of the Randi´c index, the sum-connectivity index, the harmonic index and the geometric-arithmetic index and the minimal value of the first Zagreb index and the second Zagreb index.