Abstract
In this article, we propose a quantum communication protocol via 2-step discrete time quantum walks with two coins on a graph of 10 vertices containing both cycles and paths. Quantum walks are known for their ability to integrate quantum mechanics dynamics like superposition and entanglement during the procedure. We calculate the total final quantum state of the system as well as the recovery operators to rescue the initial quantum state back at the receiver's location. Our work provides a fundamental block for a quantum teleportation scheme on a specific series of cycle and path graphs.