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Spectral properties of the non--permutability graph of subgroups | ||
| Transactions on Combinatorics | ||
| مقاله 8، دوره 11، شماره 3، آذر 2022، صفحه 281-294 اصل مقاله (466.72 K) | ||
| نوع مقاله: Workshop on Graphs, Topology and Topological Groups, Cape Town, South Africa | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2022.130027.1891 | ||
| نویسنده | ||
Seid Kassaw Muhie 
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| Department of Mathematics and Applied Mathematics, Faculty of Science, University of Cape Town, South Africa. | ||
| چکیده | ||
| Given a finite group $G$ and the subgroups lattice $\mathrm{L}(G)$ of $G$, the \textit{non--permutability graph of subgroups} $\Gamma_{\mathrm{L}(G)}$ is introduced as the graph with vertices in $\mathrm{L}(G) \setminus \mathfrak{C}_{\mathrm{L}(G)}(\mathrm{L}(G))$, where $\mathfrak{C}_{\mathrm{L}(G)}(\mathrm{L}(G))$ is the smallest sublattice of $\mathrm{L}(G)$ containing all permutable subgroups of $G$, and edges obtained by joining two vertices $X,Y$ if $XY\neq YX$. Here we study the behaviour of the non-permutability graph of subgroups using algebraic properties of associated matrices such as the adjacency and the Laplacian matrix. Further, we study the structure of some classes of groups whose non-permutability graph is strongly regular. | ||
| کلیدواژه‌ها | ||
| Subgroup commutativity degree؛ Dihedral groups؛ Sublattices؛ Adjacency Matrix؛ Regular Graph | ||
| مراجع | ||
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آمار تعداد مشاهده مقاله: 44 تعداد دریافت فایل اصل مقاله: 64 |
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