Szeged Index and Padmakar-Ivan Index of Nilpotent Graph of Integer Modulo Ring with Prime Power Order

Muhammad Naoval Husni; I Gede Adhitya Wisnu Wardhana; Putu Kartika Dewi; I Nengah Suparta

doi:10.20956/j.v20i2.31418

Authors

Muhammad Naoval Husni Universitas Mataram
I Gede Adhitya Wisnu Wardhana Universitas Mataram
Putu Kartika Dewi Universitas Pendidikan Ganesha
I Nengah Suparta Universitas Pendidikan Ganesha

DOI:

https://doi.org/10.20956/j.v20i2.31418

Keywords:

nilpotent graph, Szedge Index, Padmakar-Ivan index

Abstract

Recently, graphs have started to be used to represent a finite ring. Nikmehr and Khojasteh in the article defined the nilpotent graph of a ring . Denoted , is a graph with the set of vertices being all the elements in the ring Two vertices and are adjacent if and only if is nilpotent elements in the ring . Topological index is a field that discusses graph structure based on the degree of each vertex of a graph and the distance between vertices. In this study, the author will gives the general formula of the Szeged index and Padmakar-Ivan index of the nilpotent graph graph of the modulo ring with prime power order. The result of this research is a general formula for the topological indices of nilpotent graphs of the integer modulo ring, called the Szeged index and the Padmakar-Ivan index.

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