Beschreibung:
<jats:title>Abstract</jats:title><jats:p>We discuss the question of classifying the connected simple graphs<jats:italic>H</jats:italic>for which the second largest eigenvalue of the signless Laplacian<jats:italic>Q</jats:italic>(<jats:italic>H</jats:italic>) is ≤ 4. We discover that the question is inextricable linked to a knapsack problem with infinitely many allowed weights. We take the first few steps towards the general solution. We prove that this class of graphs is minor closed.</jats:p>