Graph Theory

This book offers a comprehensive introduction to Graph Theory, covering essential topics such as graph types, connectivity, traversals, and algorithms. It provides clear explanations and practical applications relevant to computer science, network design, and optimization problems. Each chapter includes illustrative examples, problem-solving techniques, and real-world case studies to enhance understanding and retention.

• Heuristic Algorithm For An Upper Bound
• Vertex Covering
• Types Of Enumeration
• Rooted Lebeled Tree
• Equivalance Classes Of Function
• Condensation, Reachability And Oreintable Graph
• Connected Digraphs
• Orientation Of A Graph
• Transversal Theory
• Group
• Partitions And Factorization
• Arborescence
• Coverings
• Centroid
• Types Of Digraphs
• Semi Walk Paths And Circuits And Tournaments
• Euler Digraph
• Arboricity Of Graphs
• Symmetric Graph
• Introduction To Matroids And Transversal Theory
• Lines And Points In Graphs
• Digraphs
• Permutation Group
• Unlebeled Tree
• Heuristic Algorithm For An Lower Bound
• Kuratowski’s Theorem
• Types Of Matroid
• Counting Labeled Tree
• Labeled Graph
• Cut Vertex
• Kruskal’s Algorithm
• Nullity Of A Matrix
• Permutation
• Cut Set
• Edges And Vertex
• Hand Shaking Dilemma And Directed Walk Path And Circuit
• Introduction To Graphs
• Directed And Undirected Graph
• Outer Planer Graph
• Region
• Subdivision Graphs And Inner Vertex Sets
• Basic Terminologies Of Graphs
• Types Of Graphs
• The Handshaking Lemma
• Vertices
• N-cube
• Dirac's Theorem
• The Problem Of Ramsay
• Scheduling Final Exams
• Colour Problem
• Graph Coloring
• Euler's Theorem
• Operations Of Graphs
• Fluery's Algorithm
• Graph Isomorphism
• Subgraphs
• Travelling Salesman Problem
• Planer Graphs
• Eulerial Graphs
• Problem Of Seating Arrangement
• Connected And Disconnected Graph
• Representation Of Graphs
• Hamiltonian Graphs
• Chromatic Polynomial
• Homeomorphic Graphs
• Frequency Assignments And Index Registers
• Walks Paths And Circuits
• Decomposition Theorem
• Detection Of Planarity Of A Graph
• Dual Of A Planer Graph
• Ore's Theorem
• Kuratowaski's Graph
• Konigsberg's Bridge Problem
• Bipertite Graph
• Combinatorial And Geometric Graphs
• Three Utility Problem
• Brooks’ Theorem
• Cut Matrix
• Introduction To Graph Coloring
• Chromatic Number
• Circuit Matrix
• Euler’s Formula
• Calculating A Chromatic Number
• Matrix Representation Of Graphs
• Brooks’ Theorem
• Matrices Over Gf(2) And Vector Spaces Of Graphs
• Counting Tree
• Complete Binary Tree
• Weighted Tree And Prefix Codes
• Hall's Marriage Theorem
• Transport Networks
• Infix, Prefix And Postfix Notation Of An Arithmatic Operation
• Max-flow Min-cut Theorem
• More Application Of Graph
• Reachability, Distance And Diameter, Cut Vertex, Cut Set And Bridge
• The Labeling Algorithm
• Storage Representation Of Binary Tree
• Introduction To Tree
• Binary Tree
• Spanning Tree
• Algorithm For Constructing Spanning Trees
• Dijkstra Algorithm
• Rooted Tree
• Matching Theory
• Shortest Path Algorithm
• Prim’s Algorithm
• Minimal Spanning Tree
• Binary Search Tree
• Trees And Sorting
• Traversing Binary Trees
• Huffman Code
• Tree Traversal