My group is working on ***Cordial Labeling** of 4-regular graphs.
We were wondering if someone here knows whether this study has been done before.
If not, can someone help me how to know if the given 4-regular graph admits a cordial labeling or not.

Thanks in advance.

please help, it will be much appreciated.

A function f:V→{0,1} is said to be a cordial labeling if each edge uv has the label │f(u)-f(v)│ such that, (1)The number of vertices labeled ‘0’ and the number of vertices labeled ‘1’ differ by at most “one” denoted as ││V1│-│V0││≤1. (2)The number of edges labeled ‘0’ and the number of edges labeled ‘1’ differ by at most “one” denoted as ││E1│-│E0││≤1. A graph which admits cordial labelings is called cordial.

My second question is, If i was given a 4-regular graph, how will I know if it admits a cordial labeling.

cordial labeling. Also when you say "the given 4-regular graph", are you referring to a particular graph? or do you meanagiven 4-regular graph? $\endgroup$ – Anthony Quas Aug 25 '16 at 9:16