Answer
If the graph has any other number of odd vertices besides 0 and 2, then the graph has no Euler paths and no Euler circuits.
Work Step by Step
An odd vertex is a vertex with a degree that is an odd number.
To determine if a graph has an Euler path or an Euler circuit, we need to determine the number of odd vertices in the graph. If the graph has no odd vertices, then the graph has at least one Euler path and at least one Euler circuit. If the graph has exactly 2 odd vertices, then the graph has at least one Euler path. If the graph has any other number of odd vertices (besides 0 and 2), then the graph has no Euler paths and no Euler circuits.
