Introduction to Graph Theory and its Applications

Graph Theory and its Applications

This beginner course covers the fundamental concepts in graph theory and some of its applications. Graph Theory can model and study many real-world problems and is applied in a wide range of disciplines. In computer science, graph theory is used to model networks and communications; Google search, Google maps and social medias all use it. It is used in chemistry to model molecules and in biology to study genomes. It is even used in linguistics and social sciences. Using graph theory in Machine learning and neural network is also one of the new trends.

Key Topics:

• Graph Basics
• Connectivity
• Trees
• Eulerian and Hamiltonian Graphs
• Matching and its Application
• Digraphs
• Coloring and Applications
• Planarity and Graphs on Surfaces
• Algebraic Graph Theory
• Graph Theory and Machine Learning

Course Benefits:

• Describe elements of a graph and compute its parameters
• Check for connectivity of a graph
• Explain properties of bipartite graphs and trees
• Define Eulerian and Hamiltonian graphs
• Solve some scheduling problems using graph coloring
• Explain planarity in graphs
• Represent a graph using a matrix
• Define matching in a graph
• Give real world examples of graph theory applications
• Model some simple real world problems using graphs

Course typically offered: Online, every quarter

Prerequisites: Basic knowledge in linear algebra, and familiarity with mathematical proofs and counting are recommended

Next steps: Upon completion, consider enrolling in other Applied Mathematics coursework for continued learning

Contact: For more information about this course, please contact unex-techdata@ucsd.edu