The clique number of the intersection graph of some cyclic groups

For a nontrivial finite group G, the intersection graph \Gamma(G) of G is a simple undirected graph whose vertices are the nontrivial proper subgroups of G and two vertices are joined by an edge if and only if they have a nontrivial intersection. In this paper, we obtain the clique number of the intersection graph of cyclic groups whose orders have four prime divisors. Moreover we find the clique number of the intersection graph of cyclic groups of order n such that all powers of prime divisors of n are equal. As a special case, we find the clique number of this graph for the cyclic groups of the square-free orders.

کلیدواژه ها:

Finite group ، Intersection graph ، Clique number ، cyclic group