Cordial Graph

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.

REFERENCES

Cahit, I. "Cordial Graphs: A Weaker Version of Graceful and Harmonious Graphs." Ars Combin. 23, 201-208, 1987.