2015/11/24 by Roghayeh HAFEZİEH, Hafezieh, Roghayeh
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1511.07644
openalex publication_date 2015/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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)=\χ(1) : χ∈ Irr(G)\. Let ρ(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 ρ(G)∪ (cd(G)∖\1\), such that an element p of ρ(G) is adjacent to an element m of cd(G)∖\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.