Let be a finite group. The bipartite divisor graph for the set of irreducible complex character degrees is the undirected graph with vertex set consisting of the prime numbers dividing some element of and of the nonidentity character degrees in , where a prime number is declared to be adjacent to a character degree if and only if divides . The graph is bipartite and it encodes two of the most widely studied graphs associated to the character degrees of a finite group: the prime graph and the divisor graph on the set of irreducible character degrees.
The scope of this paper is two-fold. We draw some attention to by outlining the main results that have been proved so far, see for instance [10; 11; 25; 26; 27]. In this process we improve some of these results.
"An overview on the bipartite divisor graph for the set of irreducible character degrees." Rocky Mountain J. Math. 50 (6) 2073 - 2095, December 2020. https://doi.org/10.1216/rmj.2020.50.2073