By the signless Laplacian of a (simple) graph G we mean the matrix , where A(G), D(G) denote respectively the adjacency matrix and the diagonal matrix of vertex degrees of G. It is known that connected graphs G that maximize the signless Laplacian spectral radius ฯ(Q (G)) over all connected graphs
Signless Laplacian spectral radius and Hamiltonicity
โ Scribed by Bo Zhou
- Publisher
- Elsevier Science
- Year
- 2010
- Tongue
- English
- Weight
- 112 KB
- Volume
- 432
- Category
- Article
- ISSN
- 0024-3795
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โฆ Synopsis
We give tight conditions on the signless Laplacian spectral radius of a graph for the existence of Hamiltonian paths and cycles.
๐ SIMILAR VOLUMES
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
The independence number ฮฑ(G) of G is defined as the maximum cardinality of a set of pairwise non-adjacent vertices which is called an independent set. In this paper, we characterize the graphs which have the minimum spectral radius among all the connected graphs of order n with independence number ฮฑ
Let G be a graph of order n and ฮผ(G) be the largest eigenvalue of its adjacency matrix. Let G be the complement of G. Write K n-1 + v for the complete graph on n -1 vertices together with an isolated vertex, and K n-1 + e for the complete graph on n -1 vertices with a pendent edge. We show that: