Coding in Python, we have the function to perform this task, V col_Hdeg which inputs the adjacency matrix A of the graph and initializes the array vert_color s to hold vertex colors. It then calculates the degree of each vertex and stores it in the array degrees. The while loop iterates until all vertices are colored and at each iteration, the vertex v with the highest degree is colored. The array temp is used to find the current colors of the neighbors of vertex v and an unused smallest color is determined after sorting this array.

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Polynomial Time

The problems for which the deterministic polynomial-time algorithm exists belong to the complexity class (p) and it is central in the field of computational complexity theory. According to Cobham’s thesis, polynomial time is a synonym for “feasible”, “fast”, and “efficient”.