Syllabus
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Course Code: Elective 5 MMATH21 -409 Course Name: Advanced Discrete Mathematics |
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| MODULE NO / UNIT | COURSE SYLLABUS CONTENTS OF MODULE | NOTES |
|---|---|---|
| 1 | Properties of lattice, modular and distributive lattices. Boolean algebra, basic properties, Boolean polynomial, ideals, minimal forms of Boolean polynomials. | |
| 2 | Switching circuits, application of lattice to switching circuits. | |
| 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 a n d c e n t e r s i n a t r e e , r o o t e d a n d b i n a r y t r e e . S p a n n i n g t r e e , fundamental circuits. Spanning tree in a weighted graph. Cut-sets and their properties. Fundamental circuits and cut-sets. Connectivity and separability. Network flows. |
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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 . (5.1 to 5.6, 6.4 to 6.7, 6.9, 7.1 to 7.4, 7.6, 7.8 & 7.9 o | |
