Further Results on Bond Incident Degree Indices of Molecular Trees With Perfect Matchings

In chemical graph theory, a tree with maximum degree at most four is called a molecular tree.Let T be such a tree, with edge set E(T ), and let d(u) denote the degree of a vertex u in T .A bond incident degree (BID) index of T is defined by BID ϕ (T ) = xy∈E(T ) ϕ d(x), d(y) , where ϕ is a real-valued symmetric function.The primary objective of this paper is to establish unified extremal results for BID indices of molecular trees of fixed order that admit perfect matchings, under certain conditions on ϕ.One of the main results applies, among others, to the atom-bond connectivity (ABC) index, the refined diminished Sombor index, and the atom-bond sum-connectivity (ABS) index.Another main result covers, among others, the reciprocal hyper-Zagreb index, the reciprocal reformulated first Zagreb index, the reciprocal mean square index, and the reciprocal mean cube index.The conclusions concerning the ABC and ABS indices are already known, whereas those for the other aforementioned indices are new.