Final answer:
A graph with 4 even vertices and 2 odd vertices describes an Euler path because it satisfies Euler's condition of exactly two vertices with odd degrees, which allows for an Euler path but not an Euler circuit.
Step-by-step explanation:
The question asks whether a graph with 4 even vertices and 2 odd vertices describes a Euler path or an Euler circuit. In graph theory, an Euler circuit is a path that starts and ends at the same vertex, using every edge exactly once. Conversely, an Euler path uses every edge exactly once but does not necessarily start and end at the same vertex. According to Euler's theorem:
- A graph has an Euler circuit if and only if all vertices have even degrees (an even number of edges).
- A graph has an Euler path if it has exactly two vertices of odd degree or all vertices with even degrees.
Since the given graph has exactly two vertices with an odd degree and the rest have even degrees, it satisfies one of the conditions for having an Euler path but not the condition for an Euler circuit. Therefore, the graph describes an Euler path.