@article {
author = {Kureethara, Joseph Varghese and Asok, Anjusha and Cangul, Ismail Naci},
title = {Inverse problem for the Forgotten and the hyper Zagreb indices of trees},
journal = {Communications in Combinatorics and Optimization},
volume = {7},
number = {2},
pages = {203-209},
year = {2022},
publisher = {Azarbaijan Shahid Madani University},
issn = {2538-2128},
eissn = {2538-2136},
doi = {10.22049/cco.2021.27034.1182},
abstract = {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.},
keywords = {topological index,chemical graph theory,The Forgotten Zagreb Index,The hyper Zagreb Index},
url = {http://comb-opt.azaruniv.ac.ir/article_14266.html},
eprint = {http://comb-opt.azaruniv.ac.ir/article_14266_96c5e70ed539dcd220803b9fb53ba7d2.pdf}
}