Presentation on theme: "12.3 Directed Graphs. A finite graph is a set of points, called nodes, connected by a set of lines, called edges. We can represent the graph in an adjacency."— Presentation transcript:
12.3 Directed Graphs
A finite graph is a set of points, called nodes, connected by a set of lines, called edges. We can represent the graph in an adjacency matrix. If the nodes are connected, you place a 1 in the matrix. Ex: TO: n 1 n 2 n 3 n 4 FROM: A finite graph may need to include info about direction. We get a directed graph. *Flights work this way. n1n1 n2n2 n3n3 n4n4 From Long Beach to Orlando on Jet Blue
Ex 1) Create the adjacency matrix. Chicago New York St. Louis TO: C N S FROM: What options do you have if you are making 2 flights? You would have the same matrix, but there would be two of them.
2 nd x –1 is MATRIX EDIT choose 1: [A] enter dimensions 3 × 3 Now enter each element. When done, go 2 nd MODE to QUIT Calculate [A] 2 MATRIX NAMES 1: [A] matches! If we continued this, it would be a lot of multiplying. We can use our graphing calculators to speed things up!
Ex 2) Suppose the nodes in the diagram represent people and the directed edges mean the first person knows the second person’s phone number. a) Interpret the diagram in a matrix. Al Betty Fred Charles David Ellen 2 nd person: A B C D E F 1 st person:
Ex 2) cont… b)In how many ways can a message get from Betty to Ellen in 3 or fewer calls? (*Use your calculator!) A B C D E F No ways 2 ways 1 way so 3 different ways
Ex 2) cont… c) Is it possible to get a message from Fred to Charles? If yes, what is the minimum number of calls? A B C D E F 1 call No way 2 calls 1 way Yes, 2 calls minimum