We give tight conditions on the signless Laplacian spectral radius of a graph for the existence of Hamiltonian paths and cycles.
Spectral radius and Hamiltonicity of graphs
โ Scribed by Miroslav Fiedler; Vladimir Nikiforov
- Publisher
- Elsevier Science
- Year
- 2010
- Tongue
- English
- Weight
- 91 KB
- Volume
- 432
- Category
- Article
- ISSN
- 0024-3795
No coin nor oath required. For personal study only.
โฆ Synopsis
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:
๐ SIMILAR VOLUMES
Let ฮป 1 be the largest eigenvalue and ฮป n the least eigenvalue of the adjacency matrix of a connected graph G of order n. We prove that if G is irregular with diameter D, maximum degree ฮ, minimum degree ฮด and average degree d, then . The inequality improves previous bounds of various authors and
This paper provides new upper bounds on the spectral radius \ (largest eigenvalue of the adjacency matrix) of graphs embeddable on a given compact surface. Our method is to bound the maximum rowsum in a polynomial of the adjacency matrix, using simple consequences of Euler's formula. Let # denote th