Milovanovic, EminaAltındağ, Şerife Burcu BozkurtMatejic, MarjanMilovanovic, Igor2024-01-222024-01-222023Milovanović, E., Bozkurt Altindağ, Ş.B., Matejic, M. et al.(2023). On the signless Laplacian and normalized signless Laplacian spreads of graphs. Czechoslovak Mathematical Journal, 73, 499–511 . https://doi.org/10.21136/CMJ.2023.0005-220011-46421572-9141https://doi.org/10.21136/CMJ.2023.0005-22https://hdl.handle.net/11492/7964Let G = (V, E), V = {v(1), v(2), ... , v(n)}, be a simple connected graph with n vertices, m edges and a sequence of vertex degrees d(1) >= d(2) >= ... >= d(n). Denote by A and D the adjacency matrix and diagonal vertex degree matrix of G, respectively. The signless Laplacian of G is defined as L+ = D + A and the normalized signless Laplacian matrix as L+ = D-1/2L+D-1/2. The normalized signless Laplacian spreads of a connected nonbipartite graph G are defined as r(G) = gamma(+)(2)/gamma(+ )(n)and l(G) = gamma(+)(2) - gamma(+)(n), where gamma(+ )(1)>= gamma(+)(2) >=.. . >= gamma(+)(n) >= 0 are eigenvalues of L+. We establish sharp lower and upper bounds for the normalized signless Laplacian spreads of connected graphs. In addition, we present a better lower bound on the signless Laplacian spread.enLaplacian Graph SpectraBipartite GraphSpread of GraphArticle732499511info:eu-repo/semantics/closedAccess2-s2.0-85148082637WOS:00093366900000110.21136/CMJ.2023.0005-22Q3Q4