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cse101_10_19_11

cse101_10_19_11 - Graphs 1 Map coloring a Color the map...

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Graphs 1. Map coloring a. Color the map using as few colors as possible b. Create a graph with a node for each country and an edge between neighboring countries c. Graph coloring: given, assign a color to each node such that c.i. No adjacent nodes have the same color c.ii. The minimum number of colors is used d. Scheduling exams A bunch of exams is scheduled, use as few time slots as possible. If a student is taking two exams, cannot schedule at the same time. This is a graph coloring problem. Node exam Edge between the nodes same student is taking both exams Color graph with as few colors as possible Color time slot 2. Graphs; formally a. A graph G = (V,E) has vertices (nodes) V, edges E Ex: map example V = {1,2,3,4,5,6,7} Edge x – y means “x is a neighbor of y” – symmetric relationship. So this is an undirected graph. Edges: {1,2} {1,3} {2,4} etc. b. Directed graphs Eg. The web Node URL Edge from a URL to a URL is points to (x,y) “x points to y” 3. Storing graphs on a computer a. Adjacency matrix If you have n nodes (ie. Abs(V) = n) then create an nxn matric A
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