Imagine a real-world situation that involves relationships that can be modeled with a graph. A graph consists of a discrete number of vertices and the edges that connect
Initial post + 2 responses to classmates (see attached)
Graphs for Modeling Real-World Situations
Post 1: Initial Response
Imagine a real-world situation that involves relationships that can be modeled with a graph. A graph consists of a discrete number of vertices and the edges that connect them. When brainstorming the situation you would like to model with a graph, review the examples that have been presented in your unit readings and homework exercises for ideas.
- Consider a situation in your personal or professional world that involves relationships that can be modeled with a graph. Describe this situation in at least one well-composed paragraph, sharing:
- A brief description of the situation modeled,
- What each vertex represents, and
- What each edge represents.
- Draw a connected graph using a drawing program of your choice and include it in your post. The following must be present in your graph:
- 5–10 vertices, each clearly labeled with a single capital letter (A, B, C, D, E …)
- At least 2 vertices of degree 3 or more (the degree of a vertex is the count of how many edges are attached to that vertex).
- At least 1 circuit.
View Unit 7 Discussion Post 1 example.
Post 2: Reply to a Classmate
Review a classmate's post and consider their real-world context. Address all of the following items. For all references used, please cite them in APA format. No explanations may be taken directly word for word from another source.
- In your own words, explain to your classmate what is required for a trail or circuit to be a Euler trail or circuit.
- Does a Euler trail exist for their graph? Explain specifically using the label and degree of each vertex.
- Does a Euler circuit exist for their graph? Explain specifically using the label and degree of each vertex.
View Unit 7 Discussion Post 2 example.
Post 3: Reply to Another Classmate
Review a different classmate's post and consider their real-world context. Address all of the following items. For all references used, please cite them in APA format. No explanations may be taken directly word for word from another source.
- In your own words, explain to your classmate what is required for a walk to be a Hamiltonian path or cycle.
- Identify one sequence of vertices that makes either a Hamiltonian path or a Hamiltonian cycle.
- Based on the context of your classmate's situation modeled by the graph, think about whether it would be most practical to seek a Euler trail or circuit versus a Hamiltonian path or cycle. Which one do you think would be more useful in your classmate's situation and why?
Trini Mitchell posted Jan 25, 2023 5:55 PM
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Below is my usual Saturday routes for errands and outings.
1. Home – where the heart is
2. County Dump – because the new trash company forgot they had customers
3. Lowes – gotta fix up my house for new renters
4. Walmart – nothing like surrounding myself around people I cannot relate with lol
5. Car Wash – gotta keep my baby clean and shiny
6. Cigar Lounge 1 – rest stop one just to hang out
7. Cigar Lounge 2 – rest stop 2 just to party
My route includes me starting at home, then heading to the county dump to offload weekly trash. Next is my second pace to go; Lowes, it’s my happy place. After I go to Lowes, I go to my all-time favorite place, Walmart. Now I’m heading back home to offload my purchases. Next stop is the car wash to clean my baby inside and out. Before I head to the cigar lounges, I head back home to get ready to go to my last two destinations. After my last two stops, I head back home where my heart is.
Brad Wildey posted Jan 26, 2023 7:21 PM
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Unit 7 Discussion – Graphs for Modeling Real-World Situations
Post 1
For this week’s discussion have designed a weekly travel pattern. I have plotted destinations represented by points labeled on a graph. These points are not directional and only represent normal travel patterns usually taken. I attempted to situate the points on the graph similar but not to scale on a map. Notable information regarding the travel patterns is that I frequently start at home. This is because I work from home three out of five days a week. Another interesting observation is that I never travel from church to work or to practice because those events never happen on the same day.
Here are my locations I must travel to:
Church = Church – Weekly trip on Sunday
Home = Home
Kroger = Kroger Grocery– restock on essential items
Practice= Practice – Daughter’s gymnastics practice
Sisters' = Sisters’ house – Check in see what she is up to.
Work = Work – necessary to facilitate life
The graph attached below displays a partial hub and spoke model when traveling exclusively from home. However, there are destination that are traveled on occasions that it does not makes sense to travel home based on distance. The graph shows I have six locations based on normal travel and ten routes.
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