Indifference Digraphs: A Generalization of Indifference Graphs and Semiorders

Abstract

Indifference digraphs, an analogue of indifference graphs, are introduced. They are shown to be equivalent to two restricted classes of interval digraphs, unit interval digraphs and proper interval digraphs, also introduced in this paper. These digraphs are characterized in terms of their adjacency matrices and in terms of a generalized concept of a semiorder. The results generalize the corresponding results for undirected graphs and provide a generalization of the Scott–Suppes theorem characterizing semiorders.