Cordial Digraphs

TL;DR

This paper extends the concept of cordial labelings from undirected to directed graphs, proving that directed paths and cycles are cordial and exploring the cordiality of other digraphs.

Contribution

It introduces the extension of cordial labelings to directed graphs and establishes cordiality results for paths and cycles, expanding the theory.

Findings

Directed paths are cordial

Directed cycles are cordial

Cordiality of oriented trees and other digraphs discussed

Abstract

A $(0,1)$-labeling of a set is said to be friendly if the number of elements of the set labeled 0 and the number labeled 1 differ by at most 1. Let $g$ be a labeling of the edge set of a graph that is induced by a labeling $f$ of the vertex set. If both $g$ and $f$ are friendly then $g$ is said to be a cordial labeling of the graph. We extend this concept to directed graphs and investigate the cordiality of directed graphs. We show that all directed paths and all directed cycles are cordial. We also discuss the cordiality of oriented trees and other digraphs.