Spectral Graph Theory: Course Outline (MAT 624 )
Graph Spectrum Theory:
Matrices associated to a graph, the spectrum of various graphs, diameter, regular graphs, spanning trees, complete graphs, complete bipertite graphs, Calay graphs.
Some Modules on the Applications of Spectral Graph Theory:
(Introduction to spectral geometry of graphs; Courant-Fischer theorem and graph colorings; Inequalities and bounds on eigenvalues; graph approximations; Cheeger's inequalities; Diffusion on graphs; Discretizations of heat kernels.
Energy of Graph:
Laplacian Energy, Signless Energy, Distance Energy, Normalized Laplacian Energy
He-matrix for HoneyComb Graph:
Honeycomb graph, He matrix, Spectral radius of He-matrix and bounds, He-matrix with Integer spectrum, number of triangles of He-matrix.
Energy of He-matrix for Hexagonal System:
Energy of He matrix, Upper bounds for the energy, Energy of Coalescence of graphs and various theorems.
Properties of Degree Sequences, Degree Sequences of Edge colored Graphs.