An Alternative Construction to the Transitive Closure of a Directed Graph

TL;DR

This paper introduces a novel method for constructing the transitive closure of a directed graph by adding vertices instead of arrows, preserving transitive relationships without applying universally.

Contribution

The paper presents a new vertex-adding construction for transitive closures that differs from traditional methods, applicable only to certain directed graphs.

Findings

Preserves transitive relationships in specific graphs

Offers an alternative to standard transitive closure construction

Does not apply universally to all directed graphs

Abstract

One must add arrows which are forced by transitivity to form the transitive closure of a directed graph. We introduce a construction of a transitive directed graph which is formed by adding vertices instead of arrows and which preserves the transitive relationships formed by distinct vertices in the original directed graph. Our construction does not apply to all directed graphs.