**Eulerian Graphs and Blocks** Let \( G \) be a connected graph. Prove that \( G \) is Eulerian if and only if each of the blocks of \( G \) is Eulerian. In this context, an *Eulerian graph* is a graph containing a closed trail that visits every edge of the graph exactly once. A *block* in a graph is a maximal connected subgraph that has no cut-vertex, which means it is connected and remains connected if any single vertex is removed. To prove this statement, one needs to show both directions: - If \( G \) is Eulerian, then each block of \( G \) is Eulerian. - If each block of \( G \) is Eulerian, then \( G \) is Eulerian. This involves examining the properties of Eulerian graphs, degree conditions, and the structure of blocks within the graph \( G \).

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