Graph Theory Tutorial

Graph Theory is a branch of mathematics that is concerned with the study of relationships between different objects. A graph is a collection of various vertexes also known as nodes, and these nodes are connected with each other via edges. In this tutorial, we have covered all the topics of Graph Theory like characteristics, eulerian graphs, planar graphs, special graphs, trees, paths in graph theory, etc. This Graph theory tutorial will be helpful in learning the concept of the subject along with the applications of graph theory in real life and in various fields. 

Basics of Graph Theory

• Introduction to Graph
• Basic Terminology of a Graph
• Types of a Graph
• Walks, Trails, Paths, and Circuits
• Graph Distance Components
• Cut-Vertices and Cut-Edges
• Bridge in Graph
• Independent Sets
• Shortest Path Algorithms [Dijsktra’s Algorithm]
• Application of Graph Theory
• Graph Traversals[DFS]
• Graph Traversals[BFS]

Tree

• Characterizations of Trees
• Prim’s Minimum Spanning Tree 
• Kruskal’s Minimum Spanning Tree
• Huffman Codes 
• Tree Traversals
• Traveling Salesman Problem

Special Graph

• Bipartite Graphs
• Independent Sets and Covering

Eulerian Graphs

• Eulerian Graphs
• Eulerian Graphs- Fleury’s Algorithm
• Eulerian Graphs- Chinese-Postman-Problem Hamilton

Matching

• Matching- Basics, Perfect, Bipartite
• Approximation Algorithms

Coloring

• Chromatic Numbers, Greedy Coloring Algorithm
• Edge Coloring

Planar Graph

• Planar Graph- Basics, Planarity Testing

Directed Graphs

• Directed Graphs- Degree Centrality
• Directed Graphs- Weak Connectivity
• Directed Graphs- Strong Components 
• Directed Graphs- Eulerian, Hamilton Directed Graphs
• Directed Graphs- Tarjans’ Algorithm To Find Strongly Connected Component
• Handshaking in Graph Theorem

Group Theory

• Groups, Subgroups, Semi Groups
• Isomorphism, Homomorphism
• Automorphism
• Rings, Integral Domains, Fields