Questions: Refer to the following graph. Determine whether the sequence of vertices is (a) a walk, (b) a path, and (c) a circuit in the graph. E → C → A → D → A → E (a) Is this sequence a walk?

Refer to the following graph. Determine whether the sequence of vertices is (a) a walk, (b) a path, and (c) a circuit in the graph.
E → C → A → D → A → E
(a) Is this sequence a walk?
Transcript text: Refer to the following graph. Determine whether the sequence of vertices is (a) a walk, (b) a path, and (c) a circuit in the graph. $\mathrm{E} \rightarrow \mathrm{C} \rightarrow \mathrm{A} \rightarrow \mathrm{D} \rightarrow \mathrm{A} \rightarrow \mathrm{E}$ (a) Is this sequence a walk?
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Solution

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Solution Steps

Step 1: Definition of a Walk

A walk is a sequence of vertices and edges where each edge is incident to the vertices preceding and following it.

Step 2: Check the sequence

The given sequence is E → C → A → D → A → E. Let's check if each transition corresponds to an edge in the graph:

  • E → C: There is an edge between E and C.
  • C → A: There is an edge between C and A.
  • A → D: There is an edge between A and D.
  • D → A: There is an edge between D and A.
  • A → E: There is no edge between A and E.
Step 3: Determine if it is a walk

Since there is no edge between A and E, the given sequence is not a walk.

Final Answer

No

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