2015/09/11 by Hosam Abdo, Abdo, Hosam, Darko Dimitrov +3
Computer Science · #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #cs.DM
paper · pdf · doi:10.48550/arxiv.1509.03574
13 pages, 2 Figures, 2 Tabels
arxiv created 2015/09/18 · arxiv updated 2015/09/21
In a study on the structure--dependency of the total π-electron energy from 1972, Trinajstić and one of the present authors have shown that it depends on the sums ∑v∈ Vd(v)2 and ∑v∈ Vd(v)3, where d(v) is the degree of a vertex v of the underling molecular graph G. The first sum was later named \it first Zagreb index and over the years became one of the most investigated graph--based molecular structure descriptors. On the other hand, the second sum, except in very few works on the general first Zagreb index and the zeroth--order general Randić index, has been almost completely neglected. Recently, this second sum was named \em forgotten index, or shortly the F-\em index, and shown to have an exceptional applicative potential. In this paper we examine the trees extremal with respect to the F-index.