Graph-Based Deterministic Polynomial Algorithm for NP Problems

The P vs NP problem asks whether every problem whose solution can be verified in polynomial
time (NP) can also be solved in polynomial time (P). In this paper, we present a proof that P =
NP, demonstrating that every NP problem can be solved deterministically in polynomial time using
a graph-based algorithm. We introduce a new Computation Model that enables the simulation of
a Turing machine, and show that NP problems can be simulated efficiently within this framework.
By introducing the concept of a Feasible Graph, we ensure that the simulation can be performed
in polynomial time, providing a direct path to resolving the P = NP question. Our result has
significant implications for fields such as cryptography, optimization, and artificial intelligence, where
NP-complete problems play a central role.