Bounds on graph eigenvalues II

2006/12/16 by Nikiforov, Vladimir · 15 citations
#05C50 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0612461

Abstract

Some recent results on graph eigenvalues are improved. In particular, among all graphs of given order with no cliques of order (r+1) the r-partite Turan graph has maximal spectral radius.

Cited by

• The spectral radius of 1-planar graphs without complete subgraphs
• The index of tC₃^--free signed graphs
• The α-spectral Turán type problems for graphs
• Spectral extrema of graphs of given even size forbidding H(4,3)
• Spectral radius and homeomorphically irreducible spanning trees of graphs
• Strong spectral stabilities for C_2k+1-free graphs
• Non-bipartite graphs without theta subgraphs
• Turán number of books in non-bipartite graphs
• Non-r-partite graphs without complete split subgraphs
• The spectral Turán problem: Characterizing spectral-consistent graphs
• Spectral Turán-type problem in non-r-partite graphs: Forbidden generalized book graph B_r,k
• Spectral extrema of graphs forbidding a fan
• Spectral extremal problem of the pth power of cycles
• Spectral generalized Turán problems
• Spectral extremal problems for non-bipartite graphs without odd cycles

Related

• A (forgotten) upper bound for the spectral radius of a graph
• The Moore bound for Spectral Radius
• Bounds on graph eigenvalues I
• Principal eigenvectors and principal ratios in hypergraph Turán problems
• Spectral skeletons and applications