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

• Agista Surya Bawana Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Gadjah Mada, Indonesia
• Aluysius Sutjijana Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Gadjah Mada, Indonesia
• Yeni Susanti Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Gadjah Mada, Indonesia
Keywords: dihedral groups, coprime graph, girth, independence number, Wiener index

### 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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Published
2023-09-30
How to Cite
[1]
A. Bawana, A. Sutjijana, and Y. Susanti, “ON THE GIRTH, INDEPENDENCE NUMBER, AND WIENER INDEX OF COPRIME GRAPH OF DIHEDRAL GROUP”, BAREKENG: J. Math. & App., vol. 17, no. 3, pp. 1695-1702, Sep. 2023.
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Articles