Syllabus: Incidence matrix, Adjacency matrix and Laplace matrix of a graph. The Laplace operator on graphs. Cycles and cuts. The matrix-tree theorem and Kirchoffs theorem. Dirichlet Problem. Spectral properties. Perron-Frobenius theory. Interlacing inequalities. Algebraic connectivity. Fiedlers theorem. Cheegers inequality. Graphs and electrical networks, Resistance distance. Expander graphs. Spectral gap and graph expansion. ADDITIONAL TOPICS FROM: Random walks on graphs; Eigenvalues and mixing time; Matrix games on graphs. Reference Texts: (a) R. B. Bapat: Graphs and Matrices. (b) A. Grigoryan: Introduction to Analysis on Graphs. (c) C. Godsil and D. Royle: Algebraic Graph Theory. (d) S. Jukna: Extremal Combinatorics.
https://www.isibang.ac.in/~adean/infsys/database/Bmath/AGr.html