ON THREE CONJECTURES INVOLVING THE SIGNLESS LAPLACIAN SPECTRAL RADIUS OF GRAPHS

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A survey on spectral conditions for some extremal graph problems (2021, background): “An important inequality in [72] states that q(G) ≤ 2e(G) n−1 + n − 2, which together with q(G) ≥ 2(n−2) yields that e(G) ≥ (n−1 2 ) .”
Merging the A- and Q-spectral theories (2016, background): “The remaining part of the proof uses an idea borrowed from [13].”
Sufficient spectral conditions on Hamiltonian and traceable graphs (2014, background): “The following better sharp upper bound on the signless Laplacian spectral radius for a connected graph G was given in [6], also see [4].”
Towards a spectral theory of graphs based on the signless Laplacian, I (2009, background): “In order to prove Theorem 1, the authors of [26] derive first the bound”
Towards a spectral theory of graphs based on the signless Laplacian, III (2010, background): “In order to prove Theorem 1, the authors of [26] derive first the bound”
Spectral analogues of Erdős’ and Moon–Moser’s theorems on Hamilton cycles (2015, unknown): “6 (Feng and Yu [9]).”