The Dirac operator of a graph

2013/06/10 by Oliver Knill, Knill, Oliver · 1 citation
Computer Science · Mathematics · #05C50 #15A15 #81Q10 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Graph theory and applications #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.1306.2166

openalex publication_date 2013/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We discuss some linear algebra related to the Dirac matrix D of a finite simple graph G=(V,E).

Citations

• A graph theoretical Poincare-Hopf Theorem
• The McKean-Singer Formula in Graph Theory
• On index expectation and curvature for networks
• A graph theoretical Gauss-Bonnet-Chern Theorem
• The theorems of Green-Stokes,Gauss-Bonnet and Poincare-Hopf in Graph Theory
• The Lusternik-Schnirelmann theorem for graphs
• An index formula for simple graphs

Cited by

• The Kuenneth formula for graphs

Related

• Laplace and Dirac Operators on Graphs
• Non-self-adjoint Dirac operators on graphs
• First order approach and index theorems for discrete and metric graphs
• Equivalence of lattice operators and graph matrices
• The Dirac Operator over Abelian Finite Groups