Relational data graphs and some properties of them

摘要

Data graph Γ=(C, Λ) was proposed by A. L. Rosenberg as a mathematical description for data structure. In this paper, relational data graph Γ=(C, R) is newly defined to describe and investigate more general structure represented by a generalized directed graph in which more than two equilabeled edges emanate from a node. Each element of R is a relation rather than a function on the set C of data cells. Owing to the relationality of r∈R, in relational data graphs, a set of data items can be obtained by one retrieval procedure. The authors make various formulations, which would offer effective schemes for manipulating data structures. By studying structures of a relation r∈R, the authors develop many properties characteristic to them.