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

Title

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

Creator

Kureethara J.V.; Asok A.; Cangul I.N.

Description

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. 2022 The authors.

Source

Communications in Combinatorics and Optimization, Vol-7, No. 2, pp. 203-209.

Date

2022-01-01

Publisher

Azarbaijan Shahid Madani University

Subject

The Forgotten Zagreb Index; The hyper Zagreb Index; Topological Index

Coverage

Kureethara J.V., Department of Mathematics, Christ University, Bangalore, India; Asok A., Department of Mathematics, Christ University, Bangalore, India; Cangul I.N., Department of Mathematics, Bursa Uludag University, Bursa, 16059, Turkey

Rights

Restricted Access

Relation

ISSN: 25382128

Format

Online

Language

English

Type

Article

Identifier

https://doi.org/10.22049/CCO.2021.27034.1182

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