Topological Indices of the Relative Coprime Graph of the Dihedral Group

Abdul Gazir Syarifudin; Laila Maya Santi; Andi Rafiqa Faradiyah; Verrel Rievaldo Wijaya; Erma Suwastika

doi:10.31764/jtam.v7i3.14913

Topological Indices of the Relative Coprime Graph of the Dihedral Group

Abdul Gazir Syarifudin, Laila Maya Santi, Andi Rafiqa Faradiyah, Verrel Rievaldo Wijaya, Erma Suwastika

Abstract

Assuming that G is a finite group and H is a subgroup of G, the graph known as the relative coprime graph of G with respect to H (denoted as Γ_(G,H)) has vertices corresponding to elements of G. Two distinct vertices x and y are adjacent by an edge if and only if (|x|,|y|)=1 and x or y belongs to H. This paper will focus on finding the general formula for some topological indices of the relative coprime graph of a dihedral group. The study of topological indices in graph theory offers valuable insights into the structural properties of graphs. This study is conducted by reviewing many past literatures and then from there we infer a new result. The obtained outcomes will include measurements of distance, degree of vertex, and various topological indices such as the first Zagreb index, second Zagreb index, Wiener index, and Harary index that are associated with distance and degree of vertex.

Keywords

Relative coprime graph; Dihedral group; Subgroup; Topological indices.

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DOI: https://doi.org/10.31764/jtam.v7i3.14913