Characterization of the Forgotten Topological Index and the HyperZagreb Index for the Unicyclic Graphs

Title

Characterization of the Forgotten Topological Index and the HyperZagreb Index for the Unicyclic Graphs

Creator

Asok A.; Kureethara J.V.

Description

Let G be a molecular graph with V (G) and E(G) be the vertex set and edge set, respectively. Various investigations show that many degree and distance based topological indices are used to exhibit strong intrinsic connection between the molec- ular structures and the physico-chemical properties of the chemical compounds. In this paper, we focus on two degree-based topological indices, namely, the forgotten topological index and the hyper-Zagreb Index expressed as F(G) = P u2V (G) d(u)3 and HM(G) = P uv2E(G)(d(u) + d(v))2, respectively, where d(u) and d(v) are the degrees of the vertices u and v, respectively, in the graph G. We show that the unicyclic graphs can take any even positive integer except 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 26, 28, 30, 34, 36, 38, 42, 46, 50, 50, 54, 58, 62, 66, 70, 74, 78, 86 and 94 for the forgotten index. A comparable result for the hyper-Zagreb index is also presented. 2020 University of Kragujevac, Faculty of Science. All rights reserved.

Source

Match, Vol-84, No. 3, pp. 739-751.

Date

2020-01-01

Publisher

University of Kragujevac, Faculty of Science

Coverage

Asok A., Christ University, Bangalore, India; Kureethara J.V., Christ University, Bangalore, India

Rights

Restricted Access

Relation

ISSN: 3406253

Format

Online

Language

English

Type

Article

Identifier

https://www.scopus.com/inward/record.uri?eid=2-s2.0-85101736037&partnerID=40&md5=a7e5828eb960ef9d6abe475cc39f6cbb