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The coprime prime graph of a finite group is a representation of the finite group on a graph, where the group elements are viewed as vertices of the graph, and two distinct vertices x and y are adjacent if and only if the greatest common divisor (GCD) of the orders of x and y is 1 or a prime number. This study examines the relationship between the properties of the coprime prime graph of a finite group and the properties of the finite group itself, as well as the characteristics of the coprime prime graph of a finite group that is an Euler graph for any finite group. Furthermore, the study discusses the characteristics of the coprime prime graph of the groups Zn and D2n, including connected graphs, complete graphs, planar graphs, and Hamiltonian graphs for various values of n 2 N. The study also explores the vertex connectivity of the coprime prime graph for the groups Zn and D2n for any n 2 N.
FAKULTAS SAINS DAN TEKNOLOGI, UIN SUNAN KALIJAGA YOGYAKARTA
GRAF PRIMA KOPRIMA ATAS GRUP HINGGA (Text)
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