DOI: https://doi.org/10.14710/jfma.v7i2.22552

SOMBOR INDEX AND ITS GENERALIZATION OF POWER GRAPH OF SOME GROUP WITH PRIME POWER ORDER

Rendi Bahtiar Pratama  -  Universitas Mataram, Indonesia
Fariz Maulana scopus  -  Universitas Mataram, Indonesia
Na'imah Hijriati scopus  -  Universitas Lambung Mangkurat, Indonesia
*I Gede Adhitya Wisnu Wardhana orcid scopus publons  -  Universitas Mataram, Indonesia

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Abstract
Graphs are an intriguing topic of discussion due to their numerous applications, particularly in chemistry. Topological indices derived from graph representations of molecules enable us to predict various properties of these compounds, including their physical characteristics, chemical reactivity, biological activity, toxicity, and atom-to-atom interactions. More recently, graphs have also been utilized to depict abstract mathematical objects such as groups. A notable example of graph representation in group theory is seen in power graphs. This research explores new graph topological indices based on vertex degrees, inspired by the Euclidean metric, particularly the Sombor index, and its application to the power graph of the integer modulo group and the dihedral group. The primary outcome of this study is the derivation of a general formula for the Sombor index and its generalization.
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Keywords: Power Graph; Sombor Index; Dihedral Group; Integer Modulo

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Section: FUNDAMENTAL MATHEMATICS AND APPLICATIONS
Language : EN
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