Let G be a k-connected irregular graph of order n, size m and maximum degree Δ. Let q1 be the signless Laplacian spectral radius of G. In this article, we prove the following lower bound on 2Δ - q1 : (Formula presented.) Moreover, we determine similar bounds for the signless Laplacian spectral radius of proper spanning subgraphs and k-edge-connected graphs.
Scopus Subject Areas
- Algebra and Number Theory
- irregular graph
- The signless Laplacian spectrum