Measures of closeness to cordiality for graphs

Abstract

A graph $G$ is cordial if there exists a function $f$ from the vertices of $G$ to $\{0,1\}$ such that the number of vertices labelled 0 and the number of vertices labelled 1 differ by at most 1, and if we assign to each edge $xy$ the label $|f\left(x\right)-f\left(y\right)|$, the number of edges labelled 0 and the number of edges labelled 1 also differ at most by 1. We introduce two measures of how close a graph is to being cordial, and compute these measures for a variety of classes of graphs.