Bounds and conjectures for the signless Laplacian index of graphs

Asymptotic incidence energy of lattices

“…. , n−1) [29] (See page 3323), respectively. Consequently, the signless Laplacian eigenvalues of P m P n (resp.…”

A note on two conjectures relating the independence number and spectral radius of the signless Laplacian matrix of a graph

“…Hansen and Lucas in [1] established two conjectures relating the eigenvalue q 1 and the independence number α as one can see below.…”

On a conjecture for the signless Laplacian spectral radius of cacti with given matching number

“…Recently there is a lot of work on the spectral radius or the signless Laplacian spectral radius of graphs, see [6,13,14,15,17,19,24,26,28,32,36,40,41,45,49] et al Some investigation on graphs with prefect matching or with given matching number is an important topic in the theory of graph spectra, see [7, 8, [32] determined the unique graph with the maximum signless Laplacian spectral radius among all cacti in ℓ m n with n = 2m, and gave a conjecture about the case n ≥ 2m + 1 as follows.…”