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Groups with maximum vertex degree commuting graphs
- Publication Year :
- 2019
-
Abstract
- Let $G$ be a group and $Z(G)$ be its center. We associate a commuting graph ${\Gamma}(G)$, whose vertex set is $G\setminus Z(G)$ and two distinct vertices are adjacent if they commute. We say that ${\Gamma}(G)$ is strong $k$ star free if the $k$ star graph is not a subgraph of ${\Gamma}(G)$. In this paper, we characterize all strong $5$ star free commuting graphs. As a byproduct, we classify all strong claw-free graphs. Also, we prove that the set of all non-abelian groups whose commuting graph is strong $k$ star free is finite.<br />Comment: 11 pages, 4 figures. To appear in Indian Journal of Pure and Applied Mathematics
- Subjects :
- Mathematics - Group Theory
20E99
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1908.08226
- Document Type :
- Working Paper