Course Curriculum
Course Promo | |||
Graph Theory Promo | 00:02:00 | ||
Module 01: Supplements | |||
Textbook Recommendations | 00:02:00 | ||
Tools and Softwares | 00:05:00 | ||
Sets | 00:09:00 | ||
Number Sets | 00:10:00 | ||
Parity | 00:12:00 | ||
Terminologies | 00:07:00 | ||
Module 02: Fundamentals | |||
Introduction | 00:03:00 | ||
Graphs | 00:11:00 | ||
Subgraphs | 00:09:00 | ||
Degree | 00:10:00 | ||
Sum of Degrees of Vertices Theorem | 00:23:00 | ||
Adjacency and Incidence | 00:09:00 | ||
Adjacency Matrix | 00:16:00 | ||
Incidence Matrix | 00:08:00 | ||
Isomorphism | 00:08:00 | ||
Module 03: Paths | |||
Introduction | 00:01:00 | ||
Walks, Trails, Paths, and Circuits | 00:13:00 | ||
Examples | 00:10:00 | ||
Eccentricity, Diameter, and Radius | 00:07:00 | ||
Connectedness | 00:20:00 | ||
Euler Trails and Circuits | 00:18:00 | ||
Fleury’s Algorithm | 00:10:00 | ||
Hamiltonian Paths and Circuits | 00:06:00 | ||
Ore’s Theorem | 00:14:00 | ||
Dirac’s Theorem | 00:06:00 | ||
The Shortest Path Problem | 00:16:00 | ||
Module 04: Graph Types | |||
Introduction | 00:01:00 | ||
Trivial, Null and Simple Graphs | 00:10:00 | ||
Regular Graphs | 00:10:00 | ||
Complete, Cycles and Cubic Graphs | 00:10:00 | ||
Path, Wheel and Platonic Graphs | 00:11:00 | ||
Bipartite Graphs | 00:14:00 | ||
Module 05: Trees | |||
Introduction | 00:01:00 | ||
Trees | 00:14:00 | ||
Cayley’s Theorem | 00:03:00 | ||
Rooted Trees | 00:10:00 | ||
Binary Trees | 00:14:00 | ||
Binary Tree Traversals | 00:18:00 | ||
Binary Expression Trees | 00:09:00 | ||
Binary Search Trees | 00:19:00 | ||
Spanning Trees | 00:10:00 | ||
Forest | 00:07:00 | ||
Module 06: Digraphs and Tournaments | |||
Introduction | 00:01:00 | ||
Digraphs | 00:12:00 | ||
Degree | 00:09:00 | ||
Isomorphism | 00:08:00 | ||
Adjacency Matrix | 00:10:00 | ||
Incidence Matrix | 00:05:00 | ||
Walks, Paths and Cycles | 00:12:00 | ||
Connectedness | 00:05:00 | ||
Tournaments | 00:08:00 | ||
Module 07: Planar Graphs | |||
Introduction | 00:01:00 | ||
Planar Graphs | 00:10:00 | ||
Kuratowski’s Theorem | 00:14:00 | ||
Euler’s Formula | 00:10:00 | ||
Dual Graphs | 00:11:00 | ||
Module 08: Graph Operations | |||
Introduction | 00:01:00 | ||
Vertex and Edge Deletion & Addition | 00:08:00 | ||
Cartesian Product | 00:10:00 | ||
Graph Join and Transpose | 00:04:00 | ||
Complement Graphs | 00:05:00 | ||
Module 09: Graph Colourings | |||
Introduction | 00:01:00 | ||
Vertex Colourings | 00:05:00 | ||
Edge Colourings | 00:09:00 | ||
Total Colourings | 00:05:00 |
Review
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