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

Communications in Combinatorics and Optimization

article

Kureethara, Joseph Varghese¹  Asok, Anjusha²  Cangul, Ismail Naci³ 

[1] Christ University;Department of Mathematics, Christ University;Department of Mathematics Uludag University

关键词: Topological Index;    The Forgotten Zagreb Index;    The hyper Zagreb Index;   

DOI  :  10.22049/cco.2021.27034.1182

学科分类：社会科学、人文和艺术（综合）

来源: Azarbaijan Shahide Madani Universit

【 摘 要 】

Let G = (E(G), V (G)) be a (molecular) graph with vertex set V (G) andedge set E(G). The forgotten Zagreb index and the hyper Zagreb index of G aredefined by F(G) = Pu∈V (G)d(u)3 and HM(G) = Puv∈E(G)(d(u) + d(v))2 whered(u) and d(v) are the degrees of the vertices u and v in G, respectively. A recentproblem called the inverse problem deals with the numerical realizations of topologicalindices. We see that there exist trees for all even positive integers with F(G) > 88 andwith HM(G) > 158. Along with the result, we show that there exist no trees withF(G) < 90 and HM(G) < 160 with some exceptional even positive integers and hencecharacterize the forgotten Zagreb index and the hyper Zagreb index for trees.

【 授权许可】

CC BY-SA