On the order supergraph of the power graph of a finite group

The power graph P G of a finite group G is the graph whose vertex set is G , two distinct vertices are adjacent if one is a power of the other. The order supergraph S G of P G is the graph with vertex set G , and two distinct vertices x , y are adjacent if o ( x )| o ( y ) or o ( y )| o ( x ). In this paper, we study the independence number of S G and answer a question was posed by Hamzeh and Ashrafi.