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.