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Submitted
December 7, 2023
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November 30, 2023
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Abstract

Let G be a finite group, H be a subgroup of G and g be a fixed element of G. The relative g-noncommuting graph Γ(g,H,G) of G is defined as a graph with vertex set is G and two distinct vertices x and y are adjacent if [x, y] ̸= g or [x, y] ̸= g−1, where at least x or y belong to H. In this paper, we will discuss the relative g-non-commuting graph of the dihedral groups D(2n), in particular case when n is an odd number. We give several topological indices of the relative g-noncommuting graph of the dihedral groups D2n including the first Zagreb index, Wiener index, Edge-Wiener index, Hyper-Wiener index, and Harary index.

Keywords

Relative g-noncommuting graph Dihedral group Topological indices

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How to Cite
Supu, N. A., Muchtadi-Alamsyah, I., & Suwastika, E. (2023). Topological Indices of Relative g-noncommuting Graph of Dihedral Groups. Journal of the Indonesian Mathematical Society, 29(3), 271–288. https://doi.org/10.22342/jims.29.3.1594.271-288
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