Graph Theory
Introduction to graph theory
Trees in Graph theory
Paths and Cycles in Graph theory
Graphs colouring in Graph theory
- Introduction to Graphs
- Directed and Undirected Graph
- Basic Terminologies of Graphs
- Vertices
- The Handshaking Lemma
- Types of Graphs
- N-cube
- Subgraphs
- Graph Isomorphism
- Operations of Graphs
- The Problem of Ramsay
- Connected and Disconnected Graph
- Walks Paths and Circuits
- Eulerial Graphs
- Fluery's Algorithm
- Hamiltonian Graphs
- Dirac's Theorem
- Ore's Theorem
- Problem of seating arrangement
- Travelling Salesman Problem
- Konigsberg's Bridge Problem
- Representation of Graphs
- Combinatorial and Geometric Graphs
- Planer Graphs
- Kuratowaski's Graph
- Homeomorphic Graphs
- Region
- Subdivision Graphs and Inner vertex Sets
- Outer Planer Graph
- Bipertite Graph
- Euler's Theorem
- Three utility problem
- Detection of Planarity of a Graph
- Dual of a Planer Graph
- Graph Coloring
- Chromatic Polynomial
- Decomposition theorem
- Scheduling Final Exams
- Frequency assignments and Index registers
- Colour Problem
- Introduction to Tree
- Spanning Tree
- Rooted Tree
- Binary Tree
- Traversing Binary Trees
- Counting Tree
- Tree Traversal
- Complete Binary Tree
- Infix, Prefix and Postfix Notation of an Arithmatic Operation
- Binary Search Tree
- Storage Representation of Binary Tree
- Algorithm for Constructing Spanning Trees
- Trees and Sorting
- Weighted Tree and Prefix Codes
- Huffman Code
- More Application of Graph
- Shortest Path Algorithm
- Dijkstra Algorithm
- Minimal Spanning Tree
- Prim’s algorithm
- The labeling algorithm
- Reachability, Distance and diameter, Cut vertex, cut set and bridge
- Transport Networks
- Max-Flow Min-Cut Theorem
- Matching Theory
- Hall's Marriage Theorem
- Kuratowski’s Theorem
- Cut Vertex
- Introduction to Matroids and Transversal Theory
- Types of Matroid
- Transversal Theory
- Cut Set
- Types of Enumeration
- Labeled Graph
- Counting Labeled tree
- Rooted Lebeled Tree
- Unlebeled Tree
- Centroid
- Permutation
- Permutation Group
- Equivalance classes of Function
- Group
- Symmetric Graph
- Coverings
- Vertex Covering
- Lines and Points in graphs
- Partitions and Factorization
- Arboricity of Graphs
- Digraphs
- Orientation of a graph
- Edges and Vertex
- Types of Digraphs
- Connected Digraphs
- Condensation, Reachability and Oreintable Graph
- Arborescence
- Euler Digraph
- Hand Shaking Dilemma and Directed Walk path and Circuit
- Semi walk paths and Circuits and Tournaments
- Incident, Circuit and Adjacency Matrix of Digraph
- Nullity of a Matrix
- Kruskal’s algorithm
- Heuristic algorithm for an upper bound
- Heuristic algorithm for an lower bound