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Commuting graph of a group action with few edges
- Publication Year :
- 2022
-
Abstract
- Let $A$ be a group acting by automorphisms on the group $G.$ \textit{The commuting graph $\Gamma(G,A)$ of $A$-orbits} of this action is the simple graph with vertex set $\{x^{A} : 1\ne x \in G \}$, the set of all $A$-orbits on $G\setminus \{1\}$, where two distinct vertices $x^{A}$ and $y^{A}$ are joined by an edge if and only if there exist $x_{1}\in x^{A}$ and $y_{1}\in y^{A}$ such that $[x_{1},y_{1}]=1$. The present paper characterizes the groups $G$ for which $\Gamma(G,A)$ is an $\mathcal{F}$-graph, that is, a connected graph which contains at most one vertex whose degree is not less than three.<br />Comment: 22 pages
- Subjects :
- Mathematics - Group Theory
20D10, 20D15, 20D45
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2207.03193
- Document Type :
- Working Paper