Inverse Problem for the Forgotten and the Hyper Zagreb Indices of Trees

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Kureethara J. V., Asok A., CANGÜL İ. N.

Communications in Combinatorics and Optimization, vol.7, no.2, pp.203-209, 2022 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 7 Issue: 2
  • Publication Date: 2022
  • Doi Number: 10.22049/cco.2021.27034.1182
  • Journal Name: Communications in Combinatorics and Optimization
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.203-209
  • Keywords: The Forgotten Zagreb Index, The hyper Zagreb Index, Topological Index
  • Bursa Uludag University Affiliated: Yes

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) = P u2V (G) d(u)3 and HM(G) = P uv2E(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) lt; 90 and HM(G) lt; 160 with some exceptional even positive integers and hence characterize the forgotten Zagreb index and the hyper Zagreb index for trees.