The computational complexity of cordial and equitable labelling Original Research Article

A labelling of a simple graph G=(V,E) is an assignment f of integers to the vertices of G. Under such a labelling f, we let Vi denote the set of vertices in G that are labelled i, and let Ej={{u,v}: {u,v}∈E and |f(u)−f(v)|=j}. A k-equitable labelling of a graph G=(V,E) is a labelling f : V→{0,1,…,k−1} such that, for each 0⩽i