2014/12/03 by Kung Ching Chang, Chang, Kung Ching · 3 citations
Computer Science · Mathematics · #05C50 #05C75 #58C40 #58E35 #58F05 #Combinatorics #Computer science #Constant (computer programming) #Eigenvalues and eigenvectors #Essential spectrum #FOS: Mathematics #Graph #Graph theory and applications #Laplace operator #Laplacian matrix #Line graph #Mathematical analysis #Mathematical optimization #Mathematics #Matrix Theory and Algorithms #Minimax #Multiplicity (mathematics) #Nonlinear system #Physics #Quantum mechanics #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #Spectral graph theory #Spectral theory #Spectrum (functional analysis) #Voltage graph #math.SP #msc:05C50 #msc:05C75 #msc:58C40 #msc:58E35 #msc:58F05
paper · pdf · doi:10.48550/arxiv.1412.1150
published in arXiv (Cornell University) (Cornell University)
arxiv created 2014/12/03 · openalex publication_date 2014/12/03 · arxiv updated 2016/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We develop a nonlinear spectral graph theory, in which the Laplace operator is replaced by the 1-Laplacian ?Δ1. The eigenvalue problem is to solve a nonlinear system involving a set valued function. In the study, we investigate the structure of the solutions, the minimax characterization of eigenvalues, the multiplicity theorem, etc. The eigenvalues as well as the eigenvectors are computed for several elementary graphs. The graphic feature of eigenvalues are also studied. In particular, Cheeger's constant, which has only some upper and lower bounds in linear spectral theory, equals to the first non-zero ?1Δ_ eigenvalue for connected graphs.