### Journals Information

**
Mathematics and Statistics Vol. 11(3), pp. 534 - 540 DOI: 10.13189/ms.2023.110309 Reprint (PDF) (573Kb) **

## 3-Equitable and Prime Labeling of Some Classes of Graphs

**Sangeeta ^{1}, A. Parthiban ^{2}^{,*}, P. Selvaraju ^{3}**

^{1}Department of Mathematics, Lovely Professional University, India

^{2}Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, India

^{3}Department of Mathematics, Rajalakshmi Institute of Technology, India

**ABSTRACT**

Researchers have constructed a model to transform "word motion problems into an algorithmic form" in order to be processed by an intelligent tutoring system (ITS). This process has the following steps. Step 1: Categorizing the characteristics of motion problems, step 2: suggesting a model for the categories. "In order to solve all categories of problems, graph theory including backward and forward chaining techniques of artificial intelligence can be utilized". The adoption of graph theory into motion problems has evidence that the model solves almost all of motion problems. Graph labeling is sub field of graph theory which has become the area of interest due to its diversified applications. Formally, if the nodes are labeled under some constraint, the resulting labeling is known as vertex labeling and it will be an edge labeling if the labels are assigned to edges under some conditions. Graph labeling nowadays is one of the rapid growing areas in applied mathematics which has shown its presence in almost every field. The known applications are in Computer Science, Physics, Chemistry, Radar, Coding Theory, Connectomics, Socioloy, x-ray crystallography, Astronomy etc. "For a graph G(V,E) and k > 0, give node labels from {0, 1, . . . , k − 1} such that when the edge labels are induced by the absolute value of the difference of the node labels, the count of nodes labeled with i and the count of nodes labeled with j differ by at most one and the number of lines labeled with i and with j differ by at most 1. So G with such an allocation of labels is k−equitable and becomes 3-equitable labeling, when k = 3". In this paper, the existence and non-existence of 3-equitable labeling of certain graphs are established.

**KEYWORDS**

3-equitable Graphs, Total Graph, Mycielski's Graph, Middle Graph, Central Graph, Degree Splitting Graph, Ladder Graph, Fan Graph, Friendship Graph, Lollipop Graph, Prime Labeling

**Cite This Paper in IEEE or APA Citation Styles**

(a). IEEE Format:

[1] Sangeeta , A. Parthiban , P. Selvaraju , "3-Equitable and Prime Labeling of Some Classes of Graphs," Mathematics and Statistics, Vol. 11, No. 3, pp. 534 - 540, 2023. DOI: 10.13189/ms.2023.110309.

(b). APA Format:

Sangeeta , A. Parthiban , P. Selvaraju (2023). 3-Equitable and Prime Labeling of Some Classes of Graphs. Mathematics and Statistics, 11(3), 534 - 540. DOI: 10.13189/ms.2023.110309.