Graphs with at most one signless Laplacian eigenvalue exceeding three

Abstract

We determine all connected graphs with at most one signless Laplacian eigenvalue exceeding three.

Keywords:

• signless Laplacian matrix
• signless Laplacian spectrum
• signless Laplacian eigenvalues
• forbidden subgraph
• non-bipartite graph

AMS Subject Classification:

• 05C50

Acknowledgements

We thank the referee and the editor for helpful comments and suggestions.

Notes

This work was supported by the Specialized Research Fund for the Doctoral Program of Higher Education of China [grant number 20124407110002].