We survey properties of spectra of signless Laplacians of graphs and discuss possibilities for developing a spectral theory of graphs based on this matrix. For regular graphs the whole existing theory of spectra of the adjacency matrix and of the Laplacian matrix transfers directly to the signless L
Some results on the signless Laplacians of graphs
β Scribed by Jianfeng Wang; Qiongxiang Huang; Xinhui An; Francesco Belardo
- Publisher
- Elsevier Science
- Year
- 2010
- Tongue
- English
- Weight
- 277 KB
- Volume
- 23
- Category
- Article
- ISSN
- 0893-9659
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β¦ Synopsis
In this paper we give two results concerning the signless Laplacian spectra of simple graphs. Firstly, we give a combinatorial expression for the fourth coefficient of the (signless Laplacian) characteristic polynomial of a graph. Secondly, we consider limit points for the (signless Laplacian) eigenvalues and we prove that each non-negative real number is a limit point for (signless Laplacian) eigenvalue of graphs.
π SIMILAR VOLUMES
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
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