%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