Second order Randić index of fluoranthene-type benzenoid systems

Fluoranthene-type benzenoid system are polycyclic conjugated molecules consisting of two benzenoid fragments, connected by two carbon–carbon bonds so as to form a five-membered ring. fluoranthene-type benzenoid system and its congeners are compounds which, in view of their chemical and physical properties, belong among benzenoid hydrocarbons. Let F denotes a fluoranthene-type benzenoid system, whose second order Randić index is denoted by R2(F). In this paper, we give the expression of R2(F) in terms of their inlet features. And we find the minimal and maximal value of the second order Randić index over the set of cata-catacondensed fluoranthene-type benzenoid systems, and characterize their corresponding graphs.