On the independence number of the power graph of a finite group

The power graph Gamma(G) of a finite group G is the graph whose vertex set is G, two distinct elements being adjacent if one is a power of the other. In this paper, we give sharp lower and upper bounds for the independence number of Gamma(G) and characterize the groups achieving the bounds. Moreover, we determine the independence number of Gamma(G) if G is cyclic, dihedral or generalized quaternion. Finally, we classify all finite groups G whose power graphs have independence number 3 or n 2, where n is the order of G. (C) 2018 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.