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Graph Theory

Graph TheoryMAT230 Discrete MathematicsFall 2019 MAT230 (Discrete Math) Graph TheoryFall 20191 / 72 Outline1 Definitions2 Theorems3 Representations of Graphs: Data Structures4 Traversal: eulerian and hamiltonian Graphs5 Graph Optimization6 Planarity and ColoringsMAT230 (Discrete Math) Graph TheoryFall 20192 / 72 DefinitionsDefinitionAgraphG= (V,E) consists of a setVofvertices(also callednodes)and a an edge connects to a vertex we say the edge isincidentto the vertexand say the vertex is anendpointof the an edge has only one endpoint then it is called aloop two or more edges have the same endpoints then they are (Discrete Math) Graph TheoryFall 20193 / 72 DefinitionsDefinitionTwo vertices that are joined by an edge are is a vertex that is connected to exactly one other vertexby a single a Graph is a sequence of alternating vertices and +1withn 0. Ifv1=vn+1then the walk the walk is the number of edges in the walk.

Outline 1 De nitions 2 Theorems 3 Representations of Graphs: Data Structures 4 Traversal: Eulerian and Hamiltonian Graphs 5 Graph Optimization 6 Planarity and Colorings MAT230 (Discrete Math) Graph Theory Fall 2019 2 / 72

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