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

This is the authors' abstract. We don't add key points for this paper.

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 $$E=\{((i,j),(p,q))|i,p ∈ [0,M], j,q ∈ [0,N], M,N ∈ Z,((i,j),(p,q))~{is\, an\, edge}\, i = p {and} j = q± 1 {or} i = p± 1 {and} j = q {or} i = p± 1 {and} j = q± 1\}$$ E = { ( ( i , j ) , ( p , q ) ) | i , p ∈ [ 0 , M ] , j , q ∈ [ 0 , N ] , M , N ∈ Z , ( ( i , j ) , ( p , q ) ) i s a n e d g e ⟺ 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.