bipartite divisor graph for the set of irreducible character degrees

‎let $g$ be a finite group‎. ‎we consider the set of the irreducible complex characters of $g$‎, ‎namely $irr(g)$‎, ‎and the related degree set $cd(g)={chi(1)‎ : ‎chiin irr(g)}$‎. ‎let $rho(g)$ be the set of all primes which divide some character degree of $g$‎. ‎in this paper we introduce the bipartite divisor graph for $cd(g)$ as an undirected bipartite graph with vertex set $rho(g)cup (cd(g)setminus{1})$‎, ‎such that an element $p$ of $rho(g)$ is adjacent to an element $m$ of $cd(g)setminus{1}$ if and only if $p$ divides $m$‎. ‎we denote this graph simply by $b(g)$‎. ‎then by means of combinatorial properties of this graph‎, ‎we discuss the structure of the group $g$‎. ‎in particular‎, ‎we consider the cases where $b(g)$ is a path or a cycle‎.