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Graph TheoryMAT230Discrete MathematicsFall 2019MAT230 (Discrete Math) Graph TheoryFall 20191 / 72Outline1Definitions2Theorems3Represent ations of Graphs: Data Structures4Traversal: eulerian and hamiltonian Graphs5Graph Optimization6Planarity and ColoringsMAT230 (Discrete Math) Graph TheoryFall 20192 / 72DefinitionsDefinitionAgraphG= (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 / 72DefinitionsDefinitionTwo 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

  Graph, Hamiltonian, Eulerian, Eulerian and hamiltonian graphs

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