SPECTRAL PROPERTIES OF THE NON{PERMUTABILITY GRAPH OF SUBGROUPS

Given a finite group g and the subgroups lattice 𝐿(𝐺) of 𝐺, the non-permutability graphof subgroups γ𝐿(𝐺) is introduced as the graph with vertices in 𝐿(𝐺) n c𝐿(𝐺)(𝐿(𝐺)), where c𝐿(𝐺)(𝐿(𝐺)) is the smallest sublattice of 𝐿(𝐺) containing all permutable subgroups of 𝐺, and edges obtained by joining two vertices 𝑋; 𝑌 if 𝑋𝑌 ≠ 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.