A Novel Approach to Topological Indices of the Power Graph Associated with the Dihedral Group of a Certain Order

Abdul Gazir Syarifudin; Laila Maya  Santi; Nurina Fadlila  Shaumi; Erma  Suwastika; I Gede Adhitya Wisnu  Wardhana

doi:10.29303/emj.v8i2.253

Authors

Abdul Gazir Syarifudin Department of Mathematics, Universitas Kebangsaan Republik Indonesia
Laila Maya Santi Department of Mathematics, Institut Teknologi Bandung
Nurina Fadlila Shaumi Department of Mathematics, Institut Teknologi Bandung
Erma Suwastika Department of Mathematics, Institut Teknologi Bandung
I Gede Adhitya Wisnu Wardhana Department of Mathematics, Universitas Mataram

DOI:

https://doi.org/10.29303/emj.v8i2.253

Keywords:

power graph, dihedral group, topological indices, new approach

Abstract

Power graph of a group G, represented by \Gamma_G, is a graph where the vertex set consists of the elements of G. Two distinct vertices a, b \in G are connected by an edge if and only if there exists a positive integer m such that a^m = b or b^m = a. This study explores the utilization of a new approach to compute the topological indices of power graph associated with dihedral group with n=p^k, p is primes and k \in \mathbb{Z}. Results obtained indicate that the topological indices calculated using new approach yield the same values as those obtained with the conventional approach.

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