مشخصات پژوهش

Let H be a finite group. The set of prime numbers that divide a degree of the irreducible characters of H is denoted by ρ(H). The character graph ∆(H) has been defined as a graph with the set of vertices ρ(H), and there exists an edge fr; sg in ∆(H) if there is an irreducible character of H such that its degree is divisible by rs. Here, we present several properties of ∆(H) from a graph theoretical perspective, including the number of distinct eigenvalues and cut vertices. These properties provide insight into the shape of ∆(H). Additionally, we provide bounds on the size and the matching number of ∆(H).