Brief Explanation:

Dijkstra's algorithm is used to find the shortest path between two vertices in a weighted graph. It is an algorithm that works on graphs with non-negative edge weights. The algorithm maintains a priority queue of vertices and repeatedly selects the vertex with the smallest distance from the source. It then relaxes the edges from that vertex, updating the distance to each neighboring vertex if a shorter path is found.

Explanation:

Dijkstra's algorithm is a popular algorithm used in graph theory to find the shortest path between two vertices in a weighted graph. It is applicable to graphs with non-negative edge weights. The algorithm maintains a priority queue of vertices and repeatedly selects the vertex with the smallest distance from the source.

Key Steps:
1. Initialize the distance of all vertices from the source to infinity except for the source vertex, which is initialized to 0.
2. Create a priority queue to store the vertices and their corresponding distances.
3. Insert the source vertex into the priority queue.
4. While the priority queue is not empty, do the following steps:
- Remove the vertex with the smallest distance from the priority queue.
- For each neighboring vertex of the current vertex, calculate the distance from the source through the current vertex. If this distance is smaller than the previously calculated distance, update the distance and insert the vertex into the priority queue.
5. Repeat step 4 until the priority queue is empty.
6. After the algorithm terminates, the distances of all vertices from the source will be calculated. The shortest path from the source to any other vertex can be obtained by following the path of minimum distances.

Advantages and Limitations:
- Dijkstra's algorithm guarantees finding the shortest path between two vertices in a weighted graph.
- It is efficient for sparse graphs with non-negative edge weights.
- However, it does not work correctly for graphs with negative edge weights and may not be the most efficient algorithm for dense graphs.

In conclusion, Dijkstra's algorithm is the correct option for finding the shortest path between two vertices in a weighted graph.