inverse problem for the forgotten and the hyper zagreb indices of trees

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)=∑u∈v(g)d(u)3 and hm(g)=∑uv∈e(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)<90 and hm(g)<160 with some exceptional even positive integers and hence characterize the forgotten zagreb index and the hyper zagreb index for trees.