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Let $G$ be a finite group. We consider the set of the irreducible complexcharacters of $G$, namely $Irr(G)$, and the related degree set $cd(G)=\{\chi(1): \chi\in Irr(G)\}$. Let $\rho(G)$ be the set of all primes which divide somecharacter degree of $G$. In this paper we introduce the bipartite divisor graphfor $cd(G)$ 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 anelement $m$ of $cd(G)\setminus\{1\}$ if and only if $p$ divides $m$. We denotethis graph simply by $B(G)$. Then by means of combinatorial properties of thisgraph, we discuss the structure of the group $G$. In particular, we considerthe cases where $B(G)$ is a path or a cycle.

Bipartite divisor graph for the set of irreducible character degrees