#### Answer

(a) The graph has four odd vertices. Therefore, by Euler's theorem, the graph has no Euler paths and no Euler circuits.
(b) The graph has no Euler paths and no Euler circuits.

#### Work Step by Step

(a) According to Euler's theorem, for a connected graph to have at least one Euler path, the number of odd vertices must be either 0 or 2. For a graph to have at least one Euler circuit, the number of odd vertices must be 0.
Vertex B, vertex C, vertex F, and vertex G are odd vertices. The graph has four odd vertices. Therefore, by Euler's theorem, the graph has no Euler paths and no Euler circuits.
(b) The graph has no Euler paths and no Euler circuits.