scholarly journals The signless Laplacian spectral radius of graphs with given degree sequences

2009 ◽  
Vol 157 (13) ◽  
pp. 2928-2937 ◽  
Author(s):  
Xiao-Dong Zhang
Keyword(s):  
Spectral Radius ◽  
Degree Sequences ◽  
Laplacian Spectral Radius ◽  
Signless Laplacian Spectral Radius ◽  
Signless Laplacian

Recent results on the majorization theory of graph spectrum and topological index theory

2015 ◽  
Vol 30 ◽  
Author(s):  
Muhuo Liu ◽  
Bolian Liu ◽  
Kinkar Das
Keyword(s):  
Spectral Radius ◽  
Topological Index ◽  
Index Theory ◽  
Degree Sequences ◽  
Extremal Graphs ◽  
Graph Spectrum ◽  
Laplacian Spectral Radius ◽  
Signless Laplacian Spectral Radius ◽  
Signless Laplacian ◽  
Majorization Theorem

Suppose π = (d_1,d_2,...,d_n) and π′ = (d′_1,d′_2,...,d′_n) are two positive non- increasing degree sequences, write π ⊳ π′ if and only if π \neq π′, \sum_{i=1}^n d_i = \sum_{i=1}^n d′_i, and \sum_{i=1}^j d_i ≤ \sum_{i=1}^j d′_i for all j = 1, 2, . . . , n. Let ρ(G) and μ(G) be the spectral radius and signless Laplacian spectral radius of G, respectively. Also let G and G′ be the extremal graphs with the maximal (signless Laplacian) spectral radii in the class of connected graphs with π and π′ as their degree sequences, respectively. If π ⊳ π′ can deduce that ρ(G) < ρ(G′) (respectively, μ(G) < μ(G′)), then it is said that the spectral radii (respectively, signless Laplacian spectral radii) of G and G′ satisfy the majorization theorem. This paper presents a survey to the recent results on the theory and application of the majorization theorem in graph spectrum and topological index theory.

Sign in / Sign up

Export Citation Format

Share Document