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Graph Theory - Gordon College

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.

weighted graph, then T is a minimal spanning tree of G if it is a spanning tree and no other spanning tree of G has smaller total weight. MAT230 (Discrete Math) Graph Theory Fall 2019 8 / 72. De nitions De nition The complete graph on n nodes, denoted K n, is the simple graph with

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