on bipartite divisor graph for character degrees

نویسندگان

seyed ali moosavi

چکیده

the concept of the bipartite divisor graph for integer subsets has been considered in [‎graph combinator., ‎ 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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عنوان ژورنال:
international journal of group theory

ناشر: university of isfahan

ISSN 2251-7650

دوره

شماره Articles in Press 2015

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