# ON THE GIRTH, INDEPENDENCE NUMBER, AND WIENER INDEX OF COPRIME GRAPH OF DIHEDRAL GROUP

### Abstract

*The coprime graph of a finite group * *, denoted by * *, is a graph with vertex set * * such that two distinct vertices * * and * * are adjacent if and only if their orders are coprime, i.e., * * where |x| is the order of x. In this paper, we complete the form* *of the coprime graph of a dihedral group that was given by previous research and it has been proved that * * if * *, for some * * and * * if * *. Moreover, we prove that if * * is even, then the independence number of * * is * *, where * * is the greatest odd divisor of * * and if * * is odd, then the independence number of * * is * *. Furthermore, the Wiener index of coprime graph of dihedral group has been stated here.*

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*BAREKENG: J. Math. & App.*, vol. 17, no. 3, pp. 1695-1702, Sep. 2023.

Copyright (c) 2023 Agista Surya Bawana, Aluysius Sutjijana, Yeni Susanti

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