TY - JOUR
ID - 26482
TI - Spectral properties of the non--permutability graph of subgroups
JO - Transactions on Combinatorics
JA - TOC
LA - en
SN - 2251-8657
AU - Muhie, Seid Kassaw
AD - Department of Mathematics and Applied Mathematics, Faculty of Science, University of Cape Town, South Africa.
Y1 - 2022
PY - 2022
VL - 11
IS - 3
SP - 281
EP - 294
KW - Subgroup commutativity degree
KW - Dihedral groups
KW - Sublattices
KW - Adjacency Matrix
KW - Regular graph
DO - 10.22108/toc.2022.130027.1891
N2 - 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.
UR - https://toc.ui.ac.ir/article_26482.html
L1 - https://toc.ui.ac.ir/article_26482_029aa7d1b5381d3098a7922c87fc4494.pdf
ER -