%0 Journal Article
%T Inverse problem for the Forgotten and the hyper Zagreb indices of trees
%J Communications in Combinatorics and Optimization
%I Azarbaijan Shahid Madani University
%Z 2538-2128
%A Kureethara, Joseph Varghese
%A Asok, Anjusha
%A Cangul, Ismail Naci
%D 2022
%\ 12/01/2022
%V 7
%N 2
%P 203-209
%! Inverse problem for the Forgotten and the hyper Zagreb indices of trees
%K topological index
%K chemical graph theory
%K The Forgotten Zagreb Index
%K The hyper Zagreb Index
%R 10.22049/cco.2021.27034.1182
%X 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 $F(G) = \sum_{u \in V(G)} d(u)^{3}$ and $HM(G) = \sum_{uv \in E(G)}(d(u)+d(v))^{2}$ 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.
%U http://comb-opt.azaruniv.ac.ir/article_14266_96c5e70ed539dcd220803b9fb53ba7d2.pdf