Various kinds of decipherability of codes, weaker than unique de- cipherability, have been studied since mid-1980s. We consider decipherability of directed figure codes, where directed figures are defined as labelled polyomi- noes with designated start and end points, equipped with catenation operation that may use a merging function to resolve possible conflicts. This setting ex- tends decipherability questions from words to 2D structures. In the present paper we develop a (variant of) domino graph that will allow us to decide some of the decipherability kinds by searching the graph for specific paths. Thus the main result characterizes directed figure decipherability by graph properties
