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Professor Amongus has just designed an algorithm that can take as input any undirected graph G with n vertices and a number k and determine

Professor Amongus has just designed an algorithm that can take as input any undirected graph G with n vertices and a number k and determine in O(nk) time whether G contains a clique of size k. Does Professor Amongus deserve the Turing Award for having just shown that P=NP? Why or why not ?
For answering the above question, we need to understand: What is a Clique ?
A clique, C, in an undirected graph G=(V,E) is a subset of the vertices, CsubeV, such that every two distinct vertices in the clique are adjacent. This is equivalent to the condition that the C is a subgraph of G such that C is a complete graph.
Many versions of the Clique problem are NP-hard.
k-clique decision version is NP-complete.
k-clique problem:
Input: Undirected Graph (V, E), and k
The output is a clique with k vertices, if one exists, or an error value indicating it
doesn't exist.
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