In this paper, we compute the Laplacian spectrum of non-commuting graphs of some classes of finite non-abelian groups. Our computations reveal that the non-commuting graphs of all the groups considered in this paper are L-integral. We also obtain some conditions on a group G so that its non-commuting graph is L-integral.

The set of integral ows on a nite graph ? is naturally an integral lattice 1 (?) in the Euclidean space Ker((1) of harmonic real-valued functions on the edge set of ?. Various properties of ? (bipartite character, girth, complexity, separability) are shown to correspond to properties of 1 (?) (parity, minimal norm, determinant, decomposability). The dual lattice of 1 (?) is identiied to the int...

The set of integral ows on a nite graph ? is naturally an integral lattice 1 (?) in the Euclidean space Ker((1) of harmonic real-valued functions on the edge set of ?. Various properties of ? (bipartite character, girth, complexity, separability) are shown to correspond to properties of 1 (?) (parity, minimal norm, determinant, decomposability). The dual lattice of 1 (?) is identiied to the int...