Recent advances on the bipartite divisor graph of a finite group
Gebze Technical University
Minisymposium: APPLICATIONS OF GROUPS IN GRAPH THEORY
Content: Let X be a finite set of positive integers. Let P(X) be the set of all primes dividing the elements of X and X* be the set of all elements of X different from 1. The bipartite divisor graph of X, which is denoted by B(X), has the disjoint union of P(X) with X* as its vertex set and one vertex like p from the first part (P(X)) is joined to a vertex like x in the second part (X*) if and only if p divides x. For any finite group G, there are two important sets of positive integers which are the set of conjugacy class sizes and the set of irreducible character degrees of G. In this talk we will discuss the recent advances on the bipartite divisor graph of a finite group G for these two sets of positive integers.