Todays Class How to draw a Graph Connected

Today’s Class -How to draw a Graph -Connected Graph -Complete Graph -Stencil -Quiz on Friday

Steps for creating your own Graph � 1 - Place all the vertices randomly and label each vertex. � 2 - Draw all the edges one by one. � 3 - Verify your drawing. �Example 1: Make a graph with vertices {A, B, C, D} and edges {AB, BC, BD}

Example 2: �Make a graph with vertices {A, B, C, D, E} and edges {AB, AC, AD, BB, BC, DD}

#5: �Make a graph to represent the apartment below. The vertices correspond to the rooms and the edges correspond to the doors between rooms.

#6 (04 Group) �Joseph has four friends: Anthony, Noah, Kathleen and Roberto. Kathleen is friends with each of Joseph's friends except Roberto. Noah is friends with each of Kathleen's friend. �Represent the situation using a Graph

#8 (02 Group) �Vithusan has four friends: Suzanne, Peter, Ifraha and Kayla. Ifraha is friends with Kayla and Suzanne but is not friends with Peter. Suzanne is friends with each of Ifraha's friends. Peter is friends with Kayla. �Represent the situation using a Graph

Connected Graph �when each vertex is joined to every other vertex by an edge or a series of edges Connected Graph Non-connected Graph

Connected Graph: Examples #5 Add one or more edges to create a connected graph

Connected Graph: Examples #5 Add one or more edges to create a connected graph

Complete graph: �when there is an edge between each distinct pair of vertices Complete Graph Non-complete Graph

Complete graph: Number of edges � 2 vertices �AB � 1 edge � 3 vertices �AB, AC, �BC � 2 + 1 = 3 edges

Complete graph: Number of edges � 4 vertices �AB, AC, AD, �BC, BD, �CD � 3+2+1=6 edges � 5 vertices �AB, AC, AD, AE, �BC, BD, BE, �CD, CE, �DE � 4+3+2 + 1 = 10 edges

Complete graph: Number of edges �What about n vertices? �It would be (n-1) + (n-2) + (n-3) + … + 2 + 1 �The total number of edges in a complete graph is equal to where n is the number of vertices. �Question: If the order of a complete graph is eleven, how many edges does it contain?

Complete Graph: Examples #5 Add edges to create a complete graph

Complete Graph: Examples #5 Add edges to create a complete graph

Remind �The stencils are your homework (if not finished) �Quiz #1 Friday 2016 -11 -11