Subject Code: MA7L015  Subject Name: Algebraic Graph Theory  LTP: 310  Credit:4 

Prerequisite(s): Linear Algebra (MA5L001), Discrete Mathematics (MA5L003)  
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, cospectral 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. 

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