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# Graph theory

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### Graph theory

1. 1. GRAPH THEORYANDCOMBINATORICS10CS42
2. 2. What is Graph Theory?Graph theory is the study of graphs,which are mathematical structures used tomodel pairwise relations between objects froma certain collection.
3. 3. 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.
4. 4. What are the topics we havecovered in 1st unit? Lets recallthem• 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
5. 5. Contents under 2nd Unit:• Planar & non-planar Graphs• Euler’s Formula• Detection of planarity• Graph coloring• Chromatic polynomials• Map coloring
6. 6. 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.
7. 7. Problems related to planargraphs:1.Whether complete graph K5 is planargraph or not?2.Whether complete graph K3,3 isplanar or not?
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10. 10. Platonic solids Solid bodies having faces and verticeswhich are such that(i) all faces are congurent, and(ii) the same number of faces meet at eachvertex, are called platonic solids.