The Answer to the Question
is below this banner.
Here's the Solution to this Question
This graph has an Euler path: 1-3-4-6-5-3-2-7.
It is an Euler graph, because it has an Euler cycle: 1-3-4-6-5-3-2-7-1.
This graph has an Euler path: 1-3-4-6-5-3-2.
It is a non-Euler graph, because it doesn't have an Euler cycle. The reason is vertex 1 has only one adjacent edge. In Euler cycle all vertexes must have even number of adjacent edges.
This graph doesn't have an Euler path, because all vertexes with an odd number of adjacent edges should be either start or finish, so there shouldn't be more than 2 of them. Here are 4 such vetexes.
And accordingly the graph doesn't have an Euler cycle.