Towards a spectral theory of graphs based on the signless Laplacian, II
✍ Scribed by Dragoš Cvetković; Slobodan K. Simić
- Publisher
- Elsevier Science
- Year
- 2010
- Tongue
- English
- Weight
- 228 KB
- Volume
- 432
- Category
- Article
- ISSN
- 0024-3795
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In this paper, we show that among all the connected graphs with n vertices and k cut vertices, the maximal signless Laplacian spectral radius is attained uniquely at the graph G n,k , where G n,k is obtained from the complete graph K n-k by attaching paths of almost equal lengths to all vertices of
For a (simple) graph G, the signless Laplacian of G is the matrix A(G) + D(G), where A(G) is the adjacency matrix and D(G) is the diagonal matrix of vertex degrees of G; the reduced signless Laplacian of G is the matrix (G) + B(G), where B(G) is the reduced adjacency matrix of G and (G) is the diago