Introduction:
A priority queue is a data structure that allows insertion and extraction of elements based on their priority. It is typically implemented using a heap, which ensures that the element with the highest priority is always at the front of the queue. Priority queues have various applications in computer science and can be used to solve a wide range of problems efficiently.

Detailed Explanation:
To determine which of the given options is NOT a valid application of a priority queue, let's analyze each option:

a) Dijkstra's algorithm for finding the shortest path:
Dijkstra's algorithm is a graph search algorithm that finds the shortest path between a source vertex and all other vertices in a weighted graph. The algorithm uses a priority queue to store the vertices based on their distance from the source vertex. The vertex with the lowest distance is always extracted first, allowing the algorithm to explore the graph efficiently. Thus, Dijkstra's algorithm is a valid application of a priority queue.

b) Huffman coding for data compression:
Huffman coding is a lossless data compression algorithm that assigns variable-length codes to different characters in a file based on their frequencies. The characters with higher frequencies are assigned shorter codes, resulting in efficient compression. While a priority queue is not explicitly used in the compression process, it is often used to build the Huffman tree efficiently by merging nodes with the lowest frequencies. Therefore, Huffman coding can also be considered a valid application of a priority queue.

c) Breadth-first search traversal of a graph:
Breadth-first search (BFS) is a graph traversal algorithm that explores all the vertices of a graph in breadth-first order, i.e., exploring all the neighbors of a vertex before moving on to the next level. While a priority queue can be used to improve the efficiency of BFS by selecting the next vertex to explore based on some priority, it is not a necessary component of the algorithm. BFS can be implemented using a simple queue or an array without any priority ordering. Therefore, BFS traversal is a valid application of a priority queue, but it does not necessarily require one.

d) Depth-first search traversal of a graph:
Depth-first search (DFS) is another graph traversal algorithm that explores all the vertices of a graph by recursively exploring as far as possible along each branch before backtracking. DFS does not require a priority queue as it does not depend on any priority ordering of the vertices. It can be implemented using a stack or by recursion without any need for a priority queue. Therefore, depth-first search traversal is NOT a valid application of a priority queue.

Conclusion:
In conclusion, among the given options, depth-first search traversal of a graph (option d) is NOT a valid application of a priority queue. While priority queues can be used to improve the efficiency of other graph algorithms like Dijkstra's algorithm, Huffman coding, and breadth-first search traversal, they are not necessary for implementing depth-first search.