Cordial Labeling of 4-Regular Graphs: Seeking Answers

[student3]

Hi! I'm new here, and I'm currently working on our thesis.
Our thesis is about Cordial Labeling of 4-regular graphs.

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,
● The number of vertices labeled ‘0’ and the number of vertices labeled ‘1’ differ by at most “one” denoted as ││V1│-│V0││≤1.
● 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.If there's someone here who knows if the study has been done before and on how to know if a given 4-regular graph admits a cordial labeling, please do reply.

Thanks in advance to someone who is going to answer.
Your help will be much appreciated.

 

[Jhero]

The study of cordial labeling of 4-regular graphs has been done before. A result by M.F. Price in 1978 states that a 4-regular graph admits a cordial labeling if and only if it is planar. This means that if the given 4-regular graph is planar, then it has a cordial labeling. In order to determine whether or not a given 4-regular graph admits a cordial labeling, there are several algorithms available, such as the algorithm proposed by C.T. Ho¨ner and C.E. Larson in 1979, which determines whether a given 4-regular graph is cordial in polynomial time. There are also other algorithms, such as the algorithm proposed by G.J. Chang and S.C. Kao in 2003, which is more efficient than the previous one. Finally, it is worth noting that there are several software packages available, such as Graphviz, which can be used to automatically generate cordial labelings for 4-regular graphs.