1
Graphs: introduction and basic spectral theory
▶
1.1
Basic graph theory
▶
1.1.1
Darts
1.1.2
Subgraphs
1.1.3
Walks and reachability
1.1.4
Connectedness
1.1.5
Locally finite graph, degree and regularity
1.1.6
Bipartiteness
1.1.7
Metric
1.1.8
Diameter
1.2
Space of functions on a graph
▶
1.2.1
Constant fonctions
1.2.2
Indicator functions
1.2.3
Locally constant functions
1.3
Adjacency operator
▶
1.3.1
Definition of the adjacency operator and action on constants
1.3.2
Norm of the adjacency operator
1.3.3
Adjacency operator is self-adjoint
1.3.4
From adjacency operator to graph
1.4
Permutation graphs
2
Spectral theory of regular graphs
▶
2.1
Trivial eigenvalues
2.2
The spectral gap
2.3
The infinite regular tree
▶
2.3.1
A model for the regular tree
2.3.2
The spectrum of the regular tree
Dependency graph
Friedman’s theorem: a new proof using strong convergence
Laura Monk
1
Graphs: introduction and basic spectral theory
1.1
Basic graph theory
1.1.1
Darts
1.1.2
Subgraphs
1.1.3
Walks and reachability
1.1.4
Connectedness
1.1.5
Locally finite graph, degree and regularity
1.1.6
Bipartiteness
1.1.7
Metric
1.1.8
Diameter
1.2
Space of functions on a graph
1.2.1
Constant fonctions
1.2.2
Indicator functions
1.2.3
Locally constant functions
1.3
Adjacency operator
1.3.1
Definition of the adjacency operator and action on constants
1.3.2
Norm of the adjacency operator
1.3.3
Adjacency operator is self-adjoint
1.3.4
From adjacency operator to graph
1.4
Permutation graphs
2
Spectral theory of regular graphs
2.1
Trivial eigenvalues
2.2
The spectral gap
2.3
The infinite regular tree
2.3.1
A model for the regular tree
2.3.2
The spectrum of the regular tree