Binary vertex labelings of graphs and digraphs

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 $f$ is said to be a cordial labeling of the graph. This concept extended to directed graphs is called $(2,3)$-cordiality of digraphs. We investigate the labelings that are both cordial for a graph and $(2,3)$-cordial for an orientation of it. We also consider the same problem for other known binary vertex labelings of graphs.

Received: 28 September 2023 | Accepted: 6 January 2024