Algebraic Graph Theory

Fundamental Concepts: independent sets, matchings, spanning trees, Hamiltonian cycles, Eulerian orientations, cycle covers, etc.; Operations on Graphs and the Resulting Spectra: the polynomial of a graph, eigenvalues and eigenvectors, line graphs and total graphs. etc.; The Divisor of Graphs: The divisor and cover, symmetry properties, some generalizations; Spectral Characterizations: Eigenvalues of L-, Q-, and adjacency matrix, co-spectral graphs, graphs characterized by their spectra; Spectral Techniques in Graph Theory and Combinatorics: Computing the structures suchas, independent sets, matchings, spanning trees, Hamiltonian cycles, Eulerian orientations, etc. Additional Topics: Random Graphs, Ramsey Theory, Extremal Problems.