Graph Theory part-1

• Graph Theory: 01. Seven Bridges of Konigsberg
• Graph Theory: 02. Definition of a Graph
• Graph Theory: 03. Examples of Graphs
• Graph Theory: 04. Families of Graphs
• Graph Theory: 05. Connected and Regular Graphs
• Graph Theory: 06 Sum of Degrees is ALWAYS Twice the Number of Edges
• Graph Theory: 07 Adjacency Matrix and Incidence Matrix
• Graph Theory: 08-a Basic Problem Set (part 1/2)
• Graph Theory: 08-b Basic Problem Set (part 2/2)

Graph Theory part-2

• Graph Theory: 09. Graph Isomorphisms
• Graph Theory: 10. Isomorphic and Non-Isomorphic Graphs
• BONUS: 10-b Graph Theory with Sage
• Graph Theory: 11. Neighbourhood and Bipartite Test with Colours
• Graph Theory: 12. Spanning and Induced Subgraphs
• Graph Theory: 13. Degrees at Least Two Means a Cycle Exists

Graph Theory part-3

• Graph Theory: 14a. Basic Graph Theory Problem Set 2
• Graph Theory: 14b. Basic Graph Theory Problem Set 2
• Graph Theory: 14c. Basic Graph Theory Problem Set 2
• Graph Theory: 15.There Exists a 3-Regular Graph of All Even Order at least 4
• Graph Theory: 16. Walks Trails and Paths
• Graph Theory: 17. Distance Between Vertices and Connected Components

Graph Theory part-4

• Graph Theory: 18. Every Walk Contains a Path
• Graph Theory: 19. Graph is Bipartite iff No Odd Cycle
• Graph Theory: 20. Edge Weighted Shortest Path Problem
• Graph Theory: 21. Dijkstra’s Algorithm
• Graph Theory: 22. Dijkstra Algorithm Examples

Graph Theory part-5

• Graph Theory: 23. Euler Trails and Euler Tours
• Graph Theory: 24. Euler Trail iff 0 or 2 Vertices of Odd Degree
• Graph Theory: 25. Graph Decompositions
• Graph Theory: 26. Cycle Decomposition iff All Vertices Have Even Degre
• Graph Theory: 27. Hamiltonian Graphs and Problem Set

Graph Theory part-6

• Graph Theory: 28. Hamiltonian Graph Problems
• Graph Theory: 29. Lovasz Conjecture on Hamilton Paths
• Graph Theory: 30. The 5 Known Vertex-Transitive Non-Hamiltonian Graphs
• Graph Theory: 31. Lemma on Hamiltonian Graphs
• Graph Theory: 32. Necessary (not sufficient) Condition for Existence of a Hamilton Cycle
• Graph Theory: 33. Petersen Graph is Not Hamiltonian

Graph Theory part-7

• Graph Theory: 34. Bridge edges
• Graph Theory: 35. Bridges in Connected Graphs
• Graph Theory: 36. Definition of a Tree
• Graph Theory 37. Which Graphs are Trees
• Graph Theory: 38. Three ways to Identify Trees
• Graph Theory: 39. Types of Trees
• Graph Theory: 40. Cayley’s Formula and Prufer Seqences part 1/2
• Graph Theory: 41. Cayley’s Formula and Prufer Seqences part 2/2

Graph Theory part-8

• Graph Theory: 42. Degree Sequences and Graphical Sequences
• Graph Theory: 43. Havel-Hakimi Theorem on Graphical Sequences
• Graph Theory: 44. Degree Sequence of a Tree
• Graph Theory: 45. Specific Degrees in a Tree
• Graph Theory: 46. Relation Between Minimun Degree and Subtrees
• Graph Theory: 47. Subgraphs of Regular Graphs
• Graph Theory: 48. Complement of a Graph
• Graph Theory: 49. Cartesian Product of Graphs

Graph Theory part-9

• Graph Theory: 50. Maximum vs Maximal
• Graph Theory: 51. Eccentricity, Radius & Diameter
• Graph Theory: 52. Radius and Diameter Examples
• Graph Theory: 53. Cut-Vertices
• Graph Theory: 54. Number of Cut-Vertices
• Graph Theory: 55. Bridges and Blocks
• Graph Theory: 56. Central Vertices are in a Single Block

Graph Theory part-10

• Graph Theory: 57. Planar Graphs
• Graph Theory: 58. Euler’s Formula for Plane Graphs
• Graph Theory: 59. Maximal Planar Graphs
• Graph Theory: 60. Non Planar Graphs
• Graph Theory: 61. Characterization of Planar Graphs
• Graph Theory: 62. Graph Minors and Wagner’s Theorem
• Graph Theory: 63. Petersen Graph is Non-Planar