Some Types of Spectral Distances between a Hypercube and its Complement and Line Graph

چکیده مقاله

Suppose M_'1' and M_'2' are two n×n matrices with‎ eigenvalues λ_1 (M_j)≤λ_2 (M_j)≤⋯≤λ_n (M_j), j = 1‎, ‎2. ‎The spectral distance between M_'1' and M_'2' is defined as‎: ‎ 〖σ(M_'1' ,M〗_'2' )=∑_(i=1)^n▒| λ_i (M_1 )- λ_i (M_2)|. In this paper‎, ‎the Seidel,‎ Laplacian‎, ‎ Signless Laplacian and Normalized Laplacian spectral‎ ‎distances of the hypercube and its complement‎, ‎as well as the‎ k‎-‎iterated line graphs of hypercube and its complements are‎ computed‎. ‎Some results on the spectral distance double cover are‎ also presented.‎