Final answer:
To answer the student's question, one must list the degree of each vertex in the given graph and then apply the criteria for Euler Paths and Circuits to determine their existence. The degree is the number of edges incident to a vertex, and a graph with all even-degree vertices has an Euler Circuit, while a graph with exactly two odd-degree vertices has at least one Euler Path.
Step-by-step explanation:
The question pertains to a student's work on AQR Networks and Graphs. The student is asked to analyze a given graph, write the degree for each vertex, and determine if there is an Euler Path or Euler Circuit in the graph.
The degree of a vertex in a graph is the number of edges connected to it. An Euler Path is a trail in a graph which visits every edge exactly once, but may not start and end at the same vertex. An Euler Circuit is an Euler Path that starts and ends at the same vertex.
To determine the presence of an Euler Path or Circuit, one can use the following rules: A graph has an Euler Circuit if all of its vertices have an even degree, and it has at least one Euler Path if it has exactly two vertices of odd degree. When finding the degree of each vertex, it is merely a matter of counting the number of edges incident to the vertex. If the graph does not adhere to these conditions, it neither has an Euler Path nor an Euler Circuit.