n-exact Character Graphs

2020/02/02 by Mahdi Ebrahimi, Ebrahimi, Mahdi
Mathematics · Engineering · Computer Science · #Finite Group Theory Research #graph theory and CDMA systems #Coding theory and cryptography

paper · pdf · doi:10.48550/arxiv.2002.01353

Abstract

Let Γ be a finite simple graph. If for some integer n\geqslant 4, Γ is a K_n-free graph whose complement has an odd cycle of length at least 2n-5, then we say that Γ is an n-exact graph. For a finite group G, let Δ(G) denote the character graph built on the set of degrees of the irreducible complex characters of G. In this paper, we prove that the order of an n-exact character graph is at most 2n-1. Also we determine the structure of all finite groups G with extremal n-exact character graph Δ(G).

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