Encoding paths with binary arrays in a king's graph for error-free data transmission

In this study, we have chosen the computer network with the shape of a king's graph. The king's graph G is defined as a set of edges, that is E = {((i, j), (p, q))|i, p is an element of [0, M], j, q is an element of [0, N], M, N is an element of Z,((i, j), (p, q)) is an edge double left right arrow i = p and j = q +/- 1 or i = p +/- 1 and j = q or i = p +/- 1 and j = q +/- 1}. We also set a delivery rule, in which the shortest paths in the graph are used for the message deliveries, to restrict the source consumption. Then, the paths are encoded in a way that we discover using binary arrays based on other well-known encoding methods. We prove that the path-coding method we present prevents errors denoted by false positives from the graph. Data transfer issues from computer science served as the motivation for this study.