Characterization of some finite groups by prime order element graph

For a finite group G, the prime order element graph of G, is defined as follows: the vertex set is the elements of G and two distinct vertices a and b are adjacent if and only if order of ab is prime. This graph is denoted by \Gamma(G). In this paper, we prove that the alternating groups A_۴ and A_۵, all groups of order pq, where p and q are prime numbers, and cyclic groups Z_p of prime order are uniquely characterized by the prime order element graph.

کلیدواژه ها:

finite group ، prime order element graph ، Characterization ، alternating group