Course Contents
Introduction to graphs, Simple graph, Vertices, Edges, Isomorphism, Connectedness, Adjacency, Subgraphs, Matrix representation of graph, Null graphs, Complete graphs, Cycle, Path, Wheel, Regular graph, Platonic graph, Bipartite graphs, Cubes, The complement of a simple graph, The eight circle problem, Six people at a party, The four cubes problem, Connectivity, Eulerian graphs, Hamiltonian graphs, The shortest path problem, The Chinese postman problem, The traveling salesman problem, Forest, Trees, Properties of trees, Counting trees, Minimum connecter problem, Enumeration of chemical molecule, Electrical network, Searching trees, Planar graphs, Euler’s formula, Graphs on other surfaces, Dual graphs, Infinite graphs, Colouring graphs, Colouring vertices, Brook’s theorem, Colouring maps, Colouring edges, Chromatic polynomials, Digraphs, Eulerian digraphs and tournaments.
Course Learning Outcomes
It is an introductory course in Graph Theory. After studying this course students will be able to apply the theory in solving problems in other fields such as Optimization, Chemistry, Economics etc.
Introduction graph theory lecturer 1
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Types of graph
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Problems solved in graph theory
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Simple graph
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Adjacent vertices and edges
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Adjancy matrix
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Incidence matrix
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Bipartite graph with example
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Isomorphism of graph with example
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Regular graphs with example
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Degree sequence of graph
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Example of degree sequence
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Platonic graphs
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Complement of simple graph
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Subgraph
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Cycle, path and walk in graph
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Definition of path, cycle and walk
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Wheel graph and null graph
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Hyper Cubes
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Four color cube problem
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More about four color cube problem
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Some more problems on multicolur cube
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Basic problem in graph theory set 1
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Basic problem in graph theory set 2
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Six people in a party
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Problem
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Graph connectivity
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Vertex and edge connectivity
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Cut vertex and cut edge in graph theory
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Edge Connectivity theorem
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Theorem of connected graph
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Eulerian graph
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Eulerian graph with example
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Theorem 1 on Eulerian graph
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Theorem 2
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Condition for Eulerian graph
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Hamiltonian cycle and graph
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Semi Hamiltonian graph
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Theorem on Hamiltonian graph
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Dirac theorem
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Practice problem of Hamiltonian graph
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Shortest path problem
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Network shortest path
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Chines post man problem
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Further on Chinese post man problem
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The traveling salesman problem
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Understanding of traveling salesman problem
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Forest
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Trees
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Types of tree
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Theorem on trees
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Further results on tree
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More results on topic of tree
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Spanning tree
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Example of counting spanning tree
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No of tree in complete graph
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Properties of tree
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Continue Cayley theorem
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Chemical enumeration of molecules example
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Minimum connector problem
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Cayley theorem
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Chemical enumeration of molecules
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Book Title : Introduction to Graph Theory
Author : R. J. Wilson
Edition :
Publisher : Addison Wesley
Book Title : Graphs and Diagraphs
Author : G. Chartrand and L. Lesniak
Edition :
Publisher : ACRC Press Boca Rafon
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