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arXiv · 1901.03492

4-Regular prime graphs of nonsolvable groups

Donnie Munyao Kasyoki·Paul Odhiambo Oleche
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Abstract

Let $G$ be a finite group and $\text{cd}(G)$ denote the character degree set for $G$. The prime graph $\Delta(G)$ is a simple graph whose vertex set consists of prime divisors of elements in $\text{cd}(G)$, denoted $\rho(G)$. Two primes $p,q\in \rho(G)$ are adjacent in $\Delta(G)$ if and only if $pq|a$ for some $a\in \text{cd}(G)$. We determine which simple 4-regular graphs occur as prime graphs for some finite nonsolvable group.

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Donnie Munyao Kasyoki, Paul Odhiambo Oleche. 2019-01-11. 4-Regular prime graphs of nonsolvable groups. https://arxiv.org/abs/1901.03492

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