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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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