Abstract
Let G be a simple graph of order n with m edges. Denote by (Formula presented.) the diagonal matrix of its vertex degrees and by (Formula presented.) its adjacency matrix. Then the signless Laplacian matrix of G is (Formula presented.). Let (Formula presented.) be the signless Laplacian eigenvalues of graph G and also let (Formula presented.) (Formula presented.) be the largest positive integer such that (Formula presented.). Denote by (Formula presented.) the complement graph of graph G. If (Formula presented.), then we prove that (Formula presented.). Moreover, if (Formula presented.), then (Formula presented.).
| Original language | English |
|---|---|
| Pages (from-to) | 1035-1044 |
| Number of pages | 10 |
| Journal | Linear and Multilinear Algebra |
| Volume | 69 |
| Issue number | 6 |
| DOIs | |
| State | Published - 2021 |
Keywords
- 05C50
- Graph
- Maximum degree
- Nordhaus-Gaddum-type
- Second maximum degree
- The second largest signless Laplacian eigenvalue