University of IsfahanTransactions on Combinatorics2251-865711320220901Spectral properties of the non--permutability graph of subgroups2812942648210.22108/toc.2022.130027.1891ENSeid KassawMuhieDepartment of Mathematics and Applied Mathematics, Faculty of Science, University of Cape Town, South Africa.Journal Article20210812Given 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.https://toc.ui.ac.ir/article_26482_029aa7d1b5381d3098a7922c87fc4494.pdf