Subject Code: MA7L015 Subject Name: Algebraic Graph Theory L-T-P: 3-1-0 Credit:4
Pre-requisite(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, 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.
Text Books:
  1. Bapat R. B. Graphs and Matrices, Springer
  2. Godsil C. D. and Royale G. Algebraic Graph Theory, Springer
Reference Books:
  1. Biggs N. Algebraic Graph Theory, Cambridge University Press
  2. Diestel R., Graph Theory,  Springer
  3.  Cvetković D., Doob M. and Sachs H.  Spectra of Graphs: Theory and Application, Wiley-VCH