Here's an example implementation of Dijkstra's Algorithm in JavaScript:

```
function dijkstra(graph, start, end) {
  const distances = {};
  const previous = {};
  const queue = [];

  // Initialize distances and queue
  for (let vertex in graph) {
    if (vertex === start) {
      distances[vertex] = 0;
      queue.push(vertex);
    } else {
      distances[vertex] = Infinity;
    }
    previous[vertex] = null;
  }

  // Main loop
  while (queue.length > 0) {
    const current = queue.shift();

    if (current === end) {
      // Reached the end, build and return path
      const path = [];
      let node = end;
      while (node !== start) {
        path.unshift(node);
        node = previous[node];
      }
      path.unshift(start);
      return path;
    }

    for (let neighbor in graph[current]) {
      const distance = graph[current][neighbor];
      const altDistance = distances[current] + distance;

      if (altDistance < distances[neighbor]) {
        // Found a shorter path, update distances and queue
        distances[neighbor] = altDistance;
        previous[neighbor] = current;
        queue.push(neighbor);
      }
    }
  }

  // End not reached, no path exists
  return null;
}
```

Here's how to use it with a sample graph:

```
const graph = {
  'A': { 'B': 2, 'C': 1 },
  'B': { 'A': 2, 'C': 3, 'D': 2 },
  'C': { 'A': 1, 'B': 3, 'D': 1 },
  'D': { 'B': 2, 'C': 1 }
};

const path = dijkstra(graph, 'A', 'D');
console.log(path); // ['A', 'C', 'D']
```

This implementation uses an object to represent the graph, where each key is a vertex and its value is an object of neighboring vertices and their distances. The `dijkstra` function takes this graph, a starting vertex, and an ending vertex as inputs and returns an array of vertices representing the shortest path between the start and end. If no path exists, it returns null.
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