Laplacian and Normalized Laplacian Spectral Distances of Graphs

چکیده مقاله

Suppose G1 and G2 are n- vertex graphs with Laplacian and‎ ‎normalized Laplacian eigenvalues μ i(Gj) and‎ ‎ δ(Gj) ‎, ‎ j = 1‎, ‎2 and 1 ≤ i ≤ n ‎, ‎respectively.‎ ‎We also assume that‎ ‎ μ 1(Gj) ≤μ2(Gj) ≤ ... ≤μ n(Gj), ‎δ1(Gj) ≤δ2(Gj) ≤...≤δn(Gj).‎‎The Laplacian and normalized spectral distances between G1 and‎‎ G2 are defined as follows:‎ ‎ Lσ(G1,G2) = ∑|μi(G1)‎ -μi(G2)| and lσ(G1,G2) =‎∑ |δi(G1)‎ - ‎δi(G2)|. ‎‎In this paper‎, ‎we compute the Laplacian and normalized Laplacian‎ ‎spectral distances of some particular classes of graphs‎. ‎In some‎ ‎cases‎, ‎upper and lower bounds for this quantity are supplied.‎