#### Answer

(a) This connected graph has exactly two odd vertices. Therefore, by Euler's theorem, the graph has at least one Euler path.
(b) B,A,D,C,B,D,C is an Euler path.

#### Work Step by Step

(a) Vertex B and vertex C are odd vertices. Vertex A and vertex D are even vertices. This connected graph has exactly two odd vertices. Therefore, by Euler's theorem, the graph has at least one Euler path.
(b) If a graph has exactly two odd vertices, then any Euler path starts at one odd vertex and ends at the other odd vertex.
Let's start at vertex B. From there, let's travel to vertex A, then to vertex D, then to vertex C, and then back to vertex B. There are two edges which have not been used yet. The path can then travel to vertex D and finally to vertex C.
This path is B,A,D,C,B,D,C. This path travels through every edge of the graph exactly once, so it is an Euler path.
This is one Euler path but there are other Euler paths in this graph also.