Final answer:
The question involves determining Euler Paths and Circuits by evaluating vertices' degrees within graphs and additionally discusses appropriate uses for stem-and-leaf plots, line graphs, and bar graphs.
Step-by-step explanation:
The question pertains to networks and graphs, specifically discussing an Euler Path and Circuit, and requests the degree of each vertex.
To determine whether there is an Euler Path or Circuit, we can refer to Euler's theorems which state that an Euler Path exists if a graph is connected and has exactly two vertices of odd degree, whereas an Euler Circuit exists if the graph is connected and all vertices have even degree. Writing the degree of each vertex involves enumerating the number of edges incident to each vertex.
In addition to this, when discussing various graphs such as stem-and-leaf graphs, line graphs, and bar graphs, one must consider the context. A stem-and-leaf plot is best used for small data sets to retain the original data while showing distribution. Line graphs are suitable for illustrating changes over time, and bar graphs are useful for comparing different categories or groups of data.