GRAPH THEORY ANDCOMBINATORICS10CS42

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. 

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. 

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

Contents under 2nd Unit:

• Planar & non-planar Graphs• Euler’s Formula• Detection of planarity• Graph coloring• Chromatic polynomials• Map coloring

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.

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?

1.

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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.