  We present a new model of the Discrete-Time Open Quantum Walk (DTOQW)
applicable to an arbitrary graph, thereby going beyond the case of quantum
walks on regular graphs. The impact of noise is studied by constructing Kraus
operators of different dimensions, making use of the Weyl operators. These
Kraus operators are employed as the coin operators of the DTOQW. The walker
dynamics is studied under the impact of non-Markovian amplitude damping,
depolarizing and dephasing noise channels. In addition, the walk is implemented
on arbitrary graphs, such as path graph, cycle graph, star graph, complete
graph, and complete bipartite graph. The dynamics, due to the influence of
noise, is gauged by computing the coherence and fidelity at different time
steps. Further, the probability distribution, representing the availability of
the quantum walker at different vertices of the graph, is computed at different
time steps for the above noises.
