Mathematics and Statistics Vol. 11(2), pp. 400 - 404
DOI: 10.13189/ms.2023.110219
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Inequalities for Forgotten Index of Duplication and Double Duplication of Graphs

Kalpana R , Shobana L ^*
Department of Mathematics, Faculty of Engineering and Technology, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur - 603 203, India

ABSTRACT

Molecular descriptors act as an important part in mathematical chemistry, in investigating quantitative structure-property relationship and quantitative structureactivity relationship. A topological descriptors, also called a molecular descriptor, is a mathematical formula applied to any graph which produces new molecular structure. In medicine mathematical model, the chemical compound is represented as an undirected graph, where each vertex represents an atom and each edge indicates a chemical bond between these atoms. The Wiener index is the first topological index to be used in chemistry introduced by Harold Wiener [1947]. It is used to compare the boiling points of some alkane isomers. There are various topological indices which are applied in chemistry. Among them, our interest is on Forgotten index which is degree based topological index introduced by Furtula and Gutman in 2015[2], defined as where d_u is the degree of vertex u in G. The mathematicians and chemists have studied several general properties of Forgotten index which may help the chemical and pharmaceutical industry to achieve the significance details by quantitative methods than by experiments.Vaidya et al (2009) proposed the concept of duplication of a vertex by an edge and duplication of an edge by a vertex of graphs. Shobana et al. proposed the double duplication of graphs (2017) [6]. Only connected, simple, undirected and finite graphs are considered throughout this article. Also, some inequalities are obtained by comparing the duplication and double duplication of graphs using Forgotten index which can also be used by chemists to generate new antidrug in future.

KEYWORDS
Forgotten Index, Duplication, Double Duplication, Inequality

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Kalpana R , Shobana L , "Inequalities for Forgotten Index of Duplication and Double Duplication of Graphs," Mathematics and Statistics, Vol. 11, No. 2, pp. 400 - 404, 2023. DOI: 10.13189/ms.2023.110219.

(b). APA Format:
Kalpana R , Shobana L (2023). Inequalities for Forgotten Index of Duplication and Double Duplication of Graphs. Mathematics and Statistics, 11(2), 400 - 404. DOI: 10.13189/ms.2023.110219.