Two sequences  and  sharing  elements, are said disarranged if for every non-empty subset  the sets  and  are different. In this paper we investigate properties of these pairs of sequences. Moreover, we extend the definition of disarranged pairs to a circular string of n‑sequences and prove that, for every positive integer m, except some initials values for n even, there exists a similar structure of length m.

direct product of graphs, adjacent vertex distinguishing chromatic index, cyclic permutation, derangement, disarranged sequences, 1-disarranged sequences, circular disarranged string.