Measures of closeness to cordiality for graphs

TL;DR

This paper introduces two measures to quantify how close a graph is to being cordial, providing calculations for various graph classes to understand their proximity to cordiality.

Contribution

The paper proposes novel measures of closeness to cordiality and computes these for multiple classes of graphs, advancing the understanding of graph cordiality.

Findings

Two measures of closeness to cordiality are introduced.

Calculations of these measures are provided for various graph classes.

Results show differing degrees of proximity to cordiality among graph classes.

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 $|f(x)-f(y)|$, 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.