Most Graphs are Edge-Cordial

Abstract

We extend the definition of edge-cordial graphs due to Ng and Lee for graphs on $4k$, $4k+1$, and $4k+3$ vertices to include graphs on $4k+2$ vertices, and show that, in fact, all graphs without isolated vertices are edge-cordial. Ng and Lee conjectured that all graphs on $4k$, $4k+1$, or $4k+3$ vertices are edge-cordial.