Representation of Fragmentary Structures by Oriented Graphs
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This paper investigates properties of fragmentary structures and establishes a relation between them and marked acyclic digraphs with one source and also a correspondence between classes of isomorphic fragmentary structures and unmarked acyclic digraphs of certain type, which are called feasible graphs. The concepts of a dimension of a feasible graph and its corresponding isomorphic fragmentary structures are defined. An expression is obtained for the lower-bound estimate of a dimension. A theorem on properties of feasible graphs is proved. The numbers of fragmentary structures and classes of isomorphic fragmentary structures of small dimensions are counted.
Keywordsfragmentary structure partially ordered set directed acyclic graph hypercube
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