Word Count : 639

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Let’s go step by step. --- 1. Difference between Eulerian graph and Eulerian circuit An Eulerian circuit (or Eulerian cycle) is a cycle in a graph that visits every edge exactly once and starts and ends at the same vertex. An Eulerian graph is a graph that contains an Eulerian circuit. So: - If we say "find the Eulerian circuit", we are asking for the actual cycle. - If we say "Eulerian graph", we are describing the property of having such a circuit. Euler’s theorem: A connected graph has an Eulerian circuit if and only if every vertex has even degree. --- 2. Your graph description From your notation: ``` a b c d ``` It looks like vertices are labeled `a, b, c, d`, but the edges are not listed. Since it says “graph given below” in your original problem, I assume there was a diagram. From common small examples with 4 vertices, one frequent Eulerian graph is __________ ________ _______ ______ ________ ________ ________.
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