Vertex edge graphs are part of Discrete Mathematics or Contemporary Mathematics. It is the basis for features on the Internet, credit card encryption, to the decompression and compression of video, music and photographs. It helps make communication and transportation systems more efficient - finding the shortest routes.
It is also strongly based in MP4 - Modeling with mathematics. Students have to use visual representations to solve problems and represent key ideas.
In this lesson your students will start to "decode" vertex edge graphs.
An Eularian Path is a path that travels along the edges, or lines of a figure, only once crossing through every vertex - more than once if needed. This problem stems from the famous Seven Bridges of Konigsberg.
I have my students get out the Map Coloring-Flag handout we worked on yesterday and tell them I am going to show them how to turn the flags into a map or a vertex edge graph and how to determine the number of degrees for each vertex.
I start by having my students draw a circle in the center of each section in the flags and then transferring the circles below each flag. The next step is to transfer the color in the flag to the corresponding circle below.
Check out this ShowMe for a visual description of this.
The last step is to show the students the degrees of each vertex. The degree is the number of lines going into a vertex. This is important because in the next lesson I will have students checking for an Euler path or circuit.
Student reflection increases retention and deepens critical thinking. I use a framework for reflection based on three categories. 1. content 2. collaboration 3. personal
To wrap up this lesson I asked my students to talk with their table mates by answering these questions.
1. What did you learn about vertex edge graphs?
That you can create something like a map out of a picture and its colors.
2. How was this lesson different for you? They were not working in groups but I direct taught the lesson. This is very different for my class.
I was not able to share my thoughts with someone else and that was hard.
3. How did it feel to not be able to work in a group?
I didn't like it.