Using the graph below, determine if the sequence of vertices describes an Euler path (E.P.), an Euler circuit (E.C.), or neither. P , Q , T , S , R , U , P P,Q,T,S,R,U,P

Welcome back. In this problem, we'd like to determine if our sequence of vertices describes an oiler path, oiler circuit, or neither. As a reminder, an oiler path is a path that traces along each edge of the graph exactly once, and an oiler circuit is a circuit that does the same, trace along each edge of the graph exactly once. Obviously, if it is neither, then we either don't have a path. circuit, or we have one that doesn't trace along each edge of the graph. Let's actually see what we get when we trace along this sequence of vertices. We start at P and our next vertex is Q, so we're going to travel along PQ. Our next vertex here is T, so we'll travel along QT. Next we have S, so we'll travel along TS. Then we have R, so we'll travel along SR. Then we have U, so we have to trace R U, and finally we have P, so we're gonna trace UP. Here we can see that we traced each edge of the graph exactly once, and because we have the same starting and ending vertex, this is an Euler circuit. Now some textbooks and professors do consider an oiler circuit to be an oiler path. However, the best classification for this is an oiler circuit, seeing as it is a circuit, a closed path that starts and ends at the same vertex, and it traces along each edge of the graph exactly once. So the correct answer here is oiler circuit.

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Using the graph below, determine if the sequence of vertices describes an Euler path (E.P.), an Euler circuit (E.C.), or neither.P,Q,T,S,R,U,PP,Q,T,S,R,U,P

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Using the graph below, determine if the sequence of vertices describes an Euler path (E.P.), an Euler circuit (E.C.), or neither.

$P, Q, T, S, R, U, P$