%0 Journal Article
%T Spectral properties of the non--permutability graph of subgroups
%J Transactions on Combinatorics
%I University of Isfahan
%Z 2251-8657
%A Muhie, Seid Kassaw
%D 2022
%\ 09/01/2022
%V 11
%N 3
%P 281-294
%! Spectral properties of the non--permutability graph of subgroups
%K Subgroup commutativity degree
%K Dihedral groups
%K Sublattices
%K Adjacency Matrix
%K Regular graph
%R 10.22108/toc.2022.130027.1891
%X 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.
%U https://toc.ui.ac.ir/article_26482_029aa7d1b5381d3098a7922c87fc4494.pdf