@article {
author = {Muhie, Seid},
title = {Spectral properties of the non--permutability graph of subgroups},
journal = {Transactions on Combinatorics},
volume = {11},
number = {3},
pages = {281-294},
year = {2022},
publisher = {University of Isfahan},
issn = {2251-8657},
eissn = {2251-8665},
doi = {10.22108/toc.2022.130027.1891},
abstract = {Given a finite group $G$ and the subgroups lattice $\mathrm{L}(G)$ of $G$, theĀ \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.},
keywords = {Subgroup commutativity degree,Dihedral groups,Sublattices,Adjacency Matrix,Regular graph},
url = {https://toc.ui.ac.ir/article_26482.html},
eprint = {https://toc.ui.ac.ir/article_26482_029aa7d1b5381d3098a7922c87fc4494.pdf}
}