On the graph of partial orders

Abstract

Any binary relation (where is an arbitrary set) generates a charac-teristic function on the set : If , then , otherwise . In terms of characteristic functions on the set of all binary rela-tions of the set we introduced the concept of a binary of reflexive relation of adjacency and determined the algebraic system consisting of all binary re-lations of a set and all unordered pairs of various adjacent binary rela-tions. If is finite set then this algebraic system is a graph “ a graph of graphs” in this work we investigated some features of the structures of the graph of partial orders.