Inverse problem for the Forgotten and the hyper Zagreb indices of trees

Kureethara, Joseph Varghese; Asok, Anjusha; Cangul, Ismail Naci

doi:10.22049/cco.2021.27034.1182

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	Inverse problem for the Forgotten and the hyper Zagreb indices of trees
Communications in Combinatorics and Optimization
مقاله 18، دوره 7، شماره 2، اسفند 2022، صفحه 203-209 اصل مقاله (417.36 K)
نوع مقاله: Original paper
شناسه دیجیتال (DOI): 10.22049/cco.2021.27034.1182
نویسندگان
Joseph Varghese Kureethara^* ¹؛ Anjusha Asok²؛ Ismail Naci Cangul³
¹Christ University
²Department of Mathematics, Christ University, Bangalore, India
³Department of Mathematics Uludag University, Gorukle 16059 Bursa-Turkey
چکیده
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.
کلیدواژه‌ها
Topological Index؛ Chemical Graph Theory؛ The Forgotten Zagreb Index؛ The hyper Zagreb Index

مراجع
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Inverse problem for the Forgotten and the hyper Zagreb indices of trees