The prime coprime graph Θ (G) of a finite group G is the graph whose vertex set is G and any two distinct vertices are adjacent if the greatest common divisor of their orders is either 1 or a prime. In this paper, we investigate Hamiltonicity, clique number, and vertex degree of Θ (G) for cyclic, dihedral, and dicyclic groups G. We establish that Θ (G) admits a (k, 1) -partition for cyclic, dihedral, and dicyclic groups G of specified orders.
Ranjan et al. (Mon,) studied this question.