graph theory a branch of mathematics

Question

Manu · Accepted Answer

Step 1: Identify the Starting and Ending Vertices The starting vertex is A, and we need to find the shortest path ending at vertex A. Explanation Step 2: List the Edges and Their Weights Write down all the edges with their corresponding weights: AB (Weight: 14) AC (Weight: 6) AD (Weight: 15) AE (Weight: 1) AF (Weight: 4) BC (Weight: 12) BD (Weight: 9) BE (Weight: 10) BF (Weight: 5) CD (Weight: 2) CE (Weight: 7) CF (Weight: 3) DE (Weight: 11) DF (Weight: 13) EF (Weight: 8) Explanation Step 3: Sort the Edges by Weight in Ascending Order Sort the edges based on their weights: AE (Weight: 1) CD (Weight: 2) CF (Weight: 3) AF (Weight: 4) BF (Weight: 5) AC (Weight: 6) CE (Weight: 7) EF (Weight: 8) BD (Weight: 9) BE (Weight: 10) DE (Weight: 11) BC (Weight: 12) DF (Weight: 13) AB (Weight: 14) AD (Weight: 15) Explanation Step 4: Traverse the Sorted Edges and Add to the Path Starting at vertex A, follow the sorted edges and add them to the path until reaching vertex A again. The path is formed as follows: A → E (Weight: 1) E → C (Weight: 7) C → F (Weight: 3) F → B (Weight: 5) B → D (Weight: 9) D → E (Weight: 11) E → A (Weight: 14) Explanation Step 5: Write the Path as a List of Vertices Write down the path as a list of vertices, starting and ending at vertex A: A → E → C → F → B → D → E → A Explanation Step 6: Submit the Answer Enter the path as a list of vertices: AECFBDEA Explanation Final Answer The correct shortest path starting and ending at vertex A, following the sorted edges algorithm, is: A → E → C → F → B → D → E → A

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