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   on bipartite divisor graph for character degrees  
   
نویسنده moosavi ali
منبع international journal of group theory - 2017 - دوره : 6 - شماره : 1 - صفحه:1 -7
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 nonsolvable 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.
کلیدواژه bipartite divisor graph ,character degree ,connected component ,diameter.
آدرس university of qom, department of mathematics, ایران
پست الکترونیکی s.a.mousavi@qom.ac.ir
 
     
   
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