On the Laplacian and signless Laplacian spectrum of a graph with k pairwise co-neighbor vertices
Consider the Laplacian and signless Laplacian spectrum of a graph G of order n, with k pairwise co-neighbor vertices. We prove that the number of shared neighbors is a Laplacian and a signless Laplacian eigenvalue of G with multiplicity at least k− 1. Additionally, considering a connected graph Gk w...
| Main Author: | |
|---|---|
| Other Authors: | , , , |
| Format: | article |
| Language: | eng |
| Published: |
2012
|
| Subjects: | |
| Online Access: | http://hdl.handle.net/10773/13101 |
| Country: | Portugal |
| Oai: | oai:ria.ua.pt:10773/13101 |
| Summary: | Consider the Laplacian and signless Laplacian spectrum of a graph G of order n, with k pairwise co-neighbor vertices. We prove that the number of shared neighbors is a Laplacian and a signless Laplacian eigenvalue of G with multiplicity at least k− 1. Additionally, considering a connected graph Gk with a vertex set defined by the k pairwise co-neighbor vertices of G, the Laplacian spectrum of Gk, obtained from G adding the edges of Gk, includes l + β for each nonzero Laplacian eigenvalue β of Gk. The Laplacian spectrum of G overlaps the Laplacian spectrum of Gk in at least n − k + 1 places. |
|---|