Research Information System
Communications in Combinatorics and Optimization, vol.7, no.2, pp.203-209, 2022 (ESCI)
Let G = (E(G); V (G)) be a (molecular) graph with vertex set V (G) and edge set E(G). The forgotten Zagreb index and the hyper Zagreb index of G are defined by F(G) = P u2V (G) d(u)3 and HM(G) = P uv2E(G)(d(u) + d(v))2 where d(u) and d(v) are the degrees of the vertices u and v in G, respectively. A recent problem called the inverse problem deals with the numerical realizations of topological indices. We see that there exist trees for all even positive integers with F(G) > 88 and with HM(G) > 158. Along with the result, we show that there exist no trees with F(G) lt; 90 and HM(G) lt; 160 with some exceptional even positive integers and hence characterize the forgotten Zagreb index and the hyper Zagreb index for trees.