A note on edge colorings distinguishing all triangles in a graph

TL;DR

This paper investigates edge colorings that uniquely identify all triangles in a graph, extending the concept from stars to triangles, and introduces new invariants for proper and general colorings.

Contribution

It extends the concept of distinguishing colorings from stars to triangles and provides new estimates for related invariants.

Findings

Introduces new invariants for triangle distinguishability

Extends existing theories from stars to triangles

Provides bounds for proper and general colorings

Abstract

We consider edge colorings of a graph in such a way that each two different triangles have distinct colorings. It is an extension of the well-known idea of distinguishing all maximal stars in a graph. It was introduced in literature in 1985 and studied by many authors in various variants, but always for stars. We estimate new invariants regarding triangles for proper and general colorings.