On bipartite divisor graph for character degrees

‎‎The concept of the bipartite divisor graph for integer subsets has been considered in [M‎. ‎A‎. ‎Iranmanesh and C‎. ‎E‎. ‎Praeger‎, ‎Bipartite divisor graphs for integer subsets‎, Graphs Combin.‎,  ۲۶ (۲۰۱۰) ۹۵--۱۰۵.]‎. ‎In this paper‎, ‎we will consider this graph for the set of character degrees of a finite group G and obtain some properties of this graph‎. ‎We show that if G is a solvable group‎, ‎then the number of connected components of this graph is at most ۲ and if G is a non-solvable group‎, ‎then it has at most ۳ connected components‎. ‎We also show that‎ ‎the diameter of a connected bipartite divisor graph is bounded by ۷ and obtain some properties of groups whose graphs are complete bipartite graphs‎.

کلیدواژه ها:

‎bipartite divisor graph‎ ، ‎character degree‎ ، ‎connected component‎ ، ‎diameter