Rainbow connection in some digraphs

TL;DR

This paper explores rainbow connection properties in oriented and circulant digraphs, extending previous concepts from undirected graphs and providing new results specific to these classes.

Contribution

It extends the concept of rainbow connection to circulant digraphs and presents new theoretical results in this area.

Findings

Results on rainbow connection in circulant digraphs

Extension of rainbow connection concept to oriented graphs

New theoretical bounds and properties

Abstract

An edge-coloured graph $G$ is {\it rainbow connected} if any two vertices are connected by a path whose edges have distinct colours. This concept was introduced by Chartrand et al. in \cite{ch01}, and it was extended to oriented graphs by Dorbec et al. in \cite{DI}. In this paper we present some results regarding this extention, mostly for the case of circulant digraphs.