A graph is called cordial if it is possible to label its vertices with 0s and 1s so that when the edges are labeled with the difference of the labels at their endpoints, the number of vertices (edges) labeled with ones and zeros differ at most by one. Cordial labelings were introduced by Cahit (1987) as a weakened version of graceful and harmonious.
An Eulerian graph is not cordial if the number of its vertices is multiple of four. For example, all trees
are cordial, cycle graphs of length 
are cordial if 
is not a multiple of four, complete
graphs on 
vertices are cordial if 
,
and the wheel graph on 
vertices is cordial iff 
is not congruent to 3 modulo 4.
