  Nowadays in Quantum Computing, the implementation of quantum algorithm has
created a stir since Noisy Intermediate-Scale Quantum (NISQ) devices are out in
the market. Researchers are mostly interested in solving NP-complete problems
with the help of quantum algorithms for its speed-up. As per the work on
computational complexity by Karp \cite{karp}, if any of the NP-complete problem
can be solved then any other NP-complete problem can be reduced to that problem
in polynomial time. In this Paper, $k$-coloring problem (NP-complete problem)
has been considered to solve using Grover's search. A comparator-based approach
has been used to implement $k$-coloring problem which enables the reduction of
the qubit cost compared to the state-of-the-art. An end-to-end automated
framework has been proposed to implement the $k$-coloring problem for any
unweighted and undirected graph on any available Noisy Intermediate-Scale
Quantum (NISQ) devices, which helps in generalizing our approach.
