Cordiality of Digraphs*
Published in Journal of Algebra Combinatorics Discrete Structures and Applications, 2022
Recommended citation: Beasley L, Santana M, Mousley J, and Brown D. (2022). " Cordiality of Digraphs " Journal of Algebra Combinatorics Discrete Structures and Applications. Vol 10:1.
Abstract: A (0, 1)-labelling of a set is said to be friendly if approximately one half the elements of the set are labelled 0 and one half labelled 1. Let g be a labelling of the edge set of a graph that is induced by a labelling f of the vertex set. If both g and f are friendly then g is said to be a cordial labelling of the graph. We extend this concept to directed graphs and investigate the cordiality of sets of directed graphs. We investigate a specific type of cordiality on digraphs, a restriction of quasigroup-cordiality called (2, 3)-cordiality. A directed graph is (2, 3)-cordial if there is a friendly labelling f of the vertex set which induces a (1, −1, 0)-labelling of the arc set g such that about one third of the arcs are labelled 1, about one third labelled -1 and about one third labelled 0. In particular we determine which tournaments are (2, 3)-cordial, which orientations of the n-wheel are (2, 3)-cordial, and which orientations of the n−fan are (2, 3)-cordial.