On bipartite divisor graph for character degrees

The concept of the bipartite divisor graph for integer subsets has been considered in [ýMý. ýAý. ýIranmanesh and Cý. ýEý. ýPraegerý, ýBipartite divisor graphs for integer subsetsý, ý{\em Graphs Combin.}ý, ý{\bf 26} (2010) 95--105ý.]ý. ýIn this paperý, ýwe will consider this graph for the set of character degrees of a finite group G and obtain some properties of this graphý. ýWe show that if G is a solvable groupý, ýthen the number of connected components of this graph is at most 2 and if G is a non-solvable groupý, ýthen it has at most 3 connected componentsý. ýWe also show thatý ýthe diameter of a connected bipartite divisor graph is bounded by 7 and obtain some properties of groups whose graphs are complete bipartite graphsý.