Regular Bipartite Divisor Graph

‎Given a finite group $G$‎, ‎the \textit{bipartite divisor graph}‎, ‎denoted by $B(G)$‎, ‎for its irreducible character degrees is the bipartite graph with bipartition consisting of $cd(G)^{*}$‎, ‎where $cd(G)^{*}$ denotes the nonidentity irreducible character degrees of $G$ and the $\rho(G)$ which is the set of prime numbers that divide these degrees‎, ‎and with $\{p,n\}$ being an edge if $\gcd(p,n)\neq 1$‎. ‎In this talk we consider the case that $B(G)$ is a regular graph and in particular‎, ‎the case where $B(G)$ is a cycle