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Vertex Edge Graphs - PowerPoint PPT Presentation


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Vertex Edge Graphs. Suppose you are a snowplow driver. You want to leave the garage , plow each street only once and then return to the garage. Is this always possible?. Consider this situation…. Garage. Next situation….

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Presentation Transcript
slide2

Suppose you are asnowplow driver. You want to leave the garage, plow each street only once and then return to the garage.

Is this always possible?

slide6

A vertex-edge graph

is made up of two parts:

  • Points called VERTICES
  • (each point is called a VERTEX)
  • and segments or curves
  • called EDGES
slide7

Points A and B are vertices,

the curve from A to B is an edge.

A

B

Points D and E are vertices, the segment from D to E is an edge

D

E

slide8

Point J is an EVEN VERTEX

K

J

L

If there is an even numberof edges attached to a vertex, the vertex is called an even vertex.

slide9

A

Point F is an ODD VERTEX

H

F

G

If there is an odd numberof edges attached to a vertex, the vertex is called an odd vertex.

slide10

Any edge that connects a vertex to itself is called a LOOP.

K

J

The path from K back onto itself can either be

clockwise or counterclockwise.

slide11

The degree of a vertex is the number of edges connected to that vertex.

Loops are counted twice,

once for the clockwise route and the other for the

counter-clockwise route.

slide12

C

2

4

3

D

3

A

B

E

2

Find the degree of each vertex:

slide13

D

B

C

A

E

Any route that connects one vertex to another vertexwithout repeating any edges is called a PATH.

ABC

slide14

D

B

C

A

E

AEC

slide15

D

B

C

A

E

AECD

slide16

B

C

A

E

Any path that begins and ends

at the same vertex is called a CIRCUIT.

ABCEA

slide17

I

H

F

G

Any graph that has at least one path connecting any two vertices is called a CONNECTED GRAPH.

slide18

A circuit

(beginning and ending at the same vertex)

or a path

(beginning at one vertex

and ending at another)

where each edge is used

exactly once

is called an Euler circuit

or Euler path.

slide20

C

D

2

4

4

2

2

4

E

B

F

A

To find the Adjacency Matrix of a vertex edge?

slide21

C

D

3

4

2

3

2

B

A

E

slide22

HW:

Worksheet: Paths and Circuits