The Dirac operator of a graph

Abstract

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

2 figures, 21 pages. These are expanded preparation notes to a talk given on June 5, 2013 at the Providence meeting of ILAS

References in corpus (5)

• On index expectation and curvature for networks
• The McKean-Singer Formula in Graph Theory
• An index formula for simple graphs
• The Lusternik-Schnirelmann theorem for graphs
• An integrable evolution equation in geometry

Cited by in corpus (20)

• Gauss-Bonnet for multi-linear valuations
• Coloring graphs using topology
• Universality for Barycentric subdivision
• Counting rooted forests in a network
• Graphs with Eulerian unit spheres
• Classical mathematical structures within topological graph theory
• The amazing world of simplicial complexes
• Isospectral deformations of the Dirac operator
• The strong ring of simplicial complexes
• Sphere geometry and invariants
• A Sard theorem for graph theory
• On the arithmetic of graphs
• The graph spectrum of barycentric refinements
• The Cohomology for Wu Characteristics
• The Kuenneth formula for graphs
• If Archimedes would have known functions
• More on Poincare-Hopf and Gauss-Bonnet
• Division algebra valued energized simplicial complexes
• Complexes, Graphs, Homotopy, Products and Shannon Capacity
• Graph complements of circular graphs