Given a finite group G, let cd (G) denote the set of degrees of the irreducible complex characters of G. The character degree graph of G is defined as the simple undirected graph whose vertices are the prime divisors of the numbers in cd (G) , two distinct vertices p and q being adjacent if and only if pq divides some number in cd (G). In this paper, we consider the complement of the character degree graph, and we characterize the finite groups for which this complement graph is not bipartite. This extends the analysis of Akhlaghi et al. (Proc Am Math Soc 146:1505–1513, 2018), where the solvable case was treated.
On the character degree graph of finite groups / Z. Akhlaghi, C. Casolo, S. Dolfi, E. Pacifici, L. Sanus. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - 198:5(2019 Oct), pp. 1595-1614.
On the character degree graph of finite groups
E. Pacifici
;
2019
Abstract
Given a finite group G, let cd (G) denote the set of degrees of the irreducible complex characters of G. The character degree graph of G is defined as the simple undirected graph whose vertices are the prime divisors of the numbers in cd (G) , two distinct vertices p and q being adjacent if and only if pq divides some number in cd (G). In this paper, we consider the complement of the character degree graph, and we characterize the finite groups for which this complement graph is not bipartite. This extends the analysis of Akhlaghi et al. (Proc Am Math Soc 146:1505–1513, 2018), where the solvable case was treated.File | Dimensione | Formato | |
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2019NoOddCycles.pdf
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