On extremal trees with respect to the F-index - Abdo, Hosam; Dimitrov, Darko; Gutman, Ivan (Kuwait Journal of Science, 2017)
In a study on the structure–dependency of the total π-electron energy from 1972,Trinajsti\’c and one of the present authors have shown that it depends on the sums_vVd(v)^2 and _vVd(v)^3, where d(v) is the degree of a vertex v of the underlying molecular graph G. The first sum was later named first Zagreb indexand over the years became one of the most investigated graph–based molecularstructure descriptors. On the other hand, the second sum, except in very fewworks on the general first Zagreb index and the zeroth–order general Randi\’c index, has been almost completely neglected. Recently, this second sum was namedforgotten index, or shortly the F-index, and shown to have anexceptional applicative potential. In this paper we examine the trees extremal with respect to the F-index