Course Archives Theoretical Statistics and Mathematics Unit

Course: Analysis on Graphs Level: Undergraduate Time: Currently not offered

Syllabus Past Exams 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. Top of the page Past Exams

Midterm 24.pdf Semestral 24.pdf Supplementary and Back Paper 24.pdf Top of the page

[ Semester Schedule ][ Statmath Unit ] [Indian Statistical Institute]