%0 Journal Article
%A Moosavi, S. A.
%T Groups whose Bipartite Divisor Graph for Character Degrees Has Five Vertices
%J Iranian Journal of Mathematical Sciences and Informatics
%V 17
%N 1
%U http://ijmsi.ir/article-1-1390-en.html
%R 10.52547/ijmsi.17.1.145
%D 2022
%K Bipartite divisor graph, Character degree, Solvable group.,
%X Let $G$ be a finite group and $cd^*(G)$ be the set of nonlinear irreducible character degrees of $G$. Suppose that $rho(G)$ denotes the set of primes dividing some element of $cd^*(G)$. The bipartite divisor graph for the set of character degrees which is denoted by $B(G)$, is a bipartite graph whose vertices are the disjoint union of $rho(G)$ and $cd^*(G)$, and a vertex $p in rho(G)$ is connected to a vertex $a in cd^*(G)$ if and only if $p|a$. In this paper, we investigate the structure of a group $G$ whose graph $B(G)$ has five vertices. Especially we show that all these groups are solvable.
%> http://ijmsi.ir/article-1-1390-en.pdf
%P 145-151
%& 145
%!
%9 Research paper
%L A-10-3774-1
%+ Faculty of Basic Science, University of Qom, Qom, Iran
%G eng
%@ 1735-4463
%[ 2022