On Bipartite Divisor Graph for Character Degrees
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چکیده
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., 26 (2010) 95–105.]. 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 2 and if G is a non-solvable group, then it has at most 3 connected components. We also show that the diameter of a connected bipartite divisor graph is bounded by 7 and obtain some properties of groups whose graphs are complete bipartite graphs.
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تاریخ انتشار 2016