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INDEK KONEKTIVITAS PADA GRAF KOPRIMA DARI GRUP DIHEDRAL
The coprime graph of a dihedral group is a graph constructed by representing each element of the dihedral group as a vertex, where two vertices are connected if and only if the orders of the corresponding elements are relatively prime. Based on previous research, a specific pattern was identified in the coprime graphs of dihedral groups for n = pk, showing that such graphs form a complete tripartite structure. This study aims to examine the structure and patterns of coprime graphs formed from dihedral groups with n = pk and n = pq, where p and q are odd prime numbers, and k is a positive integer. In addition, this research calculates and determines several connectivity indices of the coprime graphs of such dihedral groups, including the first and second Zagreb indices, the Wiener index, the Hyper- Wiener index, the Harary index, the Gutman index, and the Szeged index. The results obtained show that the coprime graph of the dihedral group with n = pq contains both a complete tripartite subgraph and a complete 4-partite subgraph. The values of the connectivity indices are calculated based on the degree of vertices and the distances between vertex pairs. By analyzing the partitions formed within the graph, these connectivity indices can be determined for various other values of n = pq as well.
FAKULTAS SAINS DAN TEKNOLOGI, UIN SUNAN KALIJAGA YOGYAKARTA
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