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UK - MATH 111 - Class Notes - Week 8

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UK - MATH 111 - Class Notes - Week 8

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background image Graph Theory Key Terms: Graph: a set of points and lines (the lines connect between the points) Vertices: points on a graph Edges: lines on a graph Loop: an edge that connects to the same vertex on both ends (forming a loop) Multiple Edges: when more than one edge connects to the same two vertices (bending one edge) Simple Graph: a graph that does NOT include any loops or multiple edges Path: the edges that connect vertices that can be recorded and numbered  Circuit: a path that begins and ends at the same vertex Euler Path: a path that uses every edge in the graph without repeating any edges Euler Circuit: a path that uses every edge in the graph without repeating any edges, AND starts 
and ends at the same vertex
Connected Graph: a path can be found between any pair of vertices in the graph Component: a group of vertices that form a single “piece” of the graph because they are all 
connected by edges and paths
Degree of a Vertex: the number of edges attached to a single vertex (loops count twice because 
it connects to the same vertex twice)
Degree List: a list of numbers which lists the degrees of each vertex from smallest to largest v: stands for the number of vertices Order: another word for the number of vertices e: stands for the number of edges Important information: Vertices are labeled with letters. Paths and circuits do NOT have to cover every vertex, some vertices may be left out. A graph does not have to be continuous (in one piece), it can be made up of several pieces.

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School: University of Kentucky
Department: Applied Mathematics
Course: Intro to Comtemp Math
Professor: Robert Denomme
Term: Fall 2018
Tags: graphtheory
Name: MA111
Description: Introduction to Graph Theory
Uploaded: 11/15/2018
2 Pages 60 Views 48 Unlocks
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