Graph theory
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Transcript of Graph theory
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GRAPH THEORY ANDCOMBINATORICS10CS42
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What is Graph Theory?
Graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects from a certain collection.
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Why we need to study Graph Theory?
• In computer science, graphs are used to represent networks of communication, data organization, computational devices, the flow of computation, etc. One practical example: The link structure of a website could be represented by a directed graph.
• . The vertices are the web pages available at the website and a directed edge from page A to page B exists if and only if A contains a link to B.
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What are the topics we have covered in 1st unit? Lets recall them• Directed Graphs, Undirected Graphs• Complete graph• Bipartite graph, complete bipartite graph• Regular graph• Walks, trial, circuit,path,cycle• Connected & disconnected graphs• Euler circuits & Euler trials
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Contents under 2nd Unit:
• Planar & non-planar Graphs• Euler’s Formula• Detection of planarity• Graph coloring• Chromatic polynomials• Map coloring
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Planar & non-planar graphs
• A graph which can be represented by at least one plane drawing in which the edges meet only at the vertices is called Planar graph.• A graph which can not be represented by at least one plane drawing in which the edges meet only at the vertices is called Non planar graph.
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Problems related to planar graphs:
1.Whether complete graph K5 is planar graph or not?2.Whether complete graph K3,3 is planar or not?
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Platonic solids Solid bodies having faces and vertices which are such that(i) all faces are congurent, and(ii) the same number of faces meet at each vertex, are called platonic solids.