๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Spectral radius and Hamiltonicity of graphs

โœ 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.

โœฆ 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:


๐Ÿ“œ SIMILAR VOLUMES


Signless Laplacian spectral radius and H
โœ Bo Zhou ๐Ÿ“‚ Article ๐Ÿ“… 2010 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 112 KB

We give tight conditions on the signless Laplacian spectral radius of a graph for the existence of Hamiltonian paths and cycles.

On the spectral radius of graphs
โœ Aimei Yu; Mei Lu; Feng Tian ๐Ÿ“‚ Article ๐Ÿ“… 2004 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 190 KB
The spectral radius of irregular graphs
โœ Lingsheng Shi ๐Ÿ“‚ Article ๐Ÿ“… 2009 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 135 KB

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

The Spectral Radius of Graphs on Surface
โœ M.N. Ellingham; Xiaoya Zha ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 152 KB

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