MGF 1107 Section 15.1 Graphs, Paths, and Circuits Objective 1: The ...

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Objective 2: The learner will draw a graph to model a specific situation. Example 4: Work problems 14, 16, and 19 on page 828. Objective 3: The learner will understand and use the vocabulary of graph theory. Degree of a vertex – number of edges at that vertex. Special Case: A loop contributes two to the degree. Even Vertex – has even degree. Odd Vertex – has odd degree. Example 5: Classify each vertex as even or odd. A B C D E F
Adjacent Vertices - at least one edge connects the vertices Path – a sequence of adjacent vertices and the edges connecting them. An edge can only be part of a path once but vertices can appear more than once in a path. Example 6: Use vertices to describe three paths that begin at A and end at E . A B C D E F Circuit – a path that begins and ends at the same vertex. Example 7: Use vertices to describe three circuits that begin (and end) at A . A B C D E F Connected Graph – for any two vertices, at least one path (not necessarily an edge) connects them Disconnected Graph – a graph that is not connected. A graph that is not connected has separate pieces (called components) that are connected. Example 8: Explain why graphs a and b on page 826 are connected but graphs c and d are disconnected.
Page 1: MGF 1107 Section 15.1 Graphs, Paths

MGF 1107 Section 15.1 Graphs, Paths, and Circuits Objective 1: The ...

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