Graphs with the second signless Laplacian eigenvalue ≤ 4

Abstract

We discuss the question of classifying the connected simple graphs H for which the second largest eigenvalue of the signless Laplacian Q(H) 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.

Keywords

• signless laplacian
• eigenvalues of a graph
• signless laplacian matrix
• q-eigenvalue
• second largest eigenvalue
• 05c50