Syllabus
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Course Code: MMATH21-409 Course Name: Elective V) Advanced Discrete Mathematics |
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| MODULE NO / UNIT | COURSE SYLLABUS CONTENTS OF MODULE | NOTES |
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| 1 | Properties of lattice, modular and distributive lattices. Boolean algebra, basic properties, Boolean polynomial, ideals, minimal forms of Boolean polynomials. (Chapter 1 of recommended book at Sr. No. 1) |
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| 2 | Switching circuits, application of lattice to switching circuits. (2.1 of chapter 2 of recommended book at Sr. No. 1) |
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| 3 | Finite and infinite graphs, Incidence and degree, Isolated vertex, pendant vertex, Null graph, isomosphism, subgraphs, a puzzle with multicolored cubes, walks, paths and circuits. Connected and disconnected graphs, Components of a graph, Euler graphs, Hamiltonian paths and circuits, The traveling salesman problem. Trees and their properties, pendant vertices in a tree, distance and centers in a tree, rooted and binary tree. Spanning tree, fundamental circuits. Spanning tree in a weighted graph. Cut-sets and their properties. Fundamental circuits and cut-sets. Connectivity and separability. Network flows. (1.1 to 1.5, 2.1 to 2.10, 3.1 to 3.10, 4.1 to 4.6 of recommended book at Sr. No. 2) |
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| 4 | Planner graphs. Kuratowski’s two graphs. Representation of planner graphs. Euler formula for planner graphs. Geometric dual, vector and vector spaces, Vector space associated with a graph. Basis vectors of a graph. Circuit and cut-set subspaces. Intersection and joins of WC and WS. Incidence matrix, submatrices of A(G), Circuit matrix, Fundamental circuit matrix, and its rank, Cut-set matrix, path matrix and adjacency matrix . |
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