Prime Cordial Labeling of Some Graphs

In this paper we prove that the split graphs of 1,n K and are prime cordial graphs. We also show that the square graph of is a prime cordial graph while middle graph of is a prime cordial graph for . Further we prove that the wheel graph admits prime cordial labeling for . , n n B n  , n n B n P 8 4 n 


Introduction
We begin with simple, finite, connected and undirected graph with vertices and edges.For standard terminology and notations we follow Gross and Yellen [1].We will provide brief summary of definitions and other information which are necessary for the present investigations.
Definition 1.1 If the vertices are assigned values subject to certain condition(s) then it is known as graph labeling.
Any graph labeling will have the following three common characteristics: 1) A set of numbers from which vertex labels are chosen; 2) A rule that assigns a value to each edge; 3) A condition that this value has to satisfy.According to Beineke and Hegde [2] graph labeling serves as a frontier between number theory and structure of graphs.For a dynamic survey of various graph labeling problems along with extensive bibliography we refer to Gallian [3].
Definition 1.2 A mapping is called binary vertex labeling of and number of vertices of having label under where 0 and 1 number of edges of having label under *

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The concept of cordial labeling was introduced by Cahit [4].Some labeling schemes are also introduced with minor variations in cordial theme.Some of them are product cordial labeling, total product cordial labeling and prime cordial labeling.The present work is focused on prime cordial labeling.Definition 1.5 A prime cordial labeling of a graph with vertex set is a bijection paper we obtain some new prime cordial graphs.
A graph which admits prime cordial labeling is called a prime cordial graph.
The concept of prime cordial labeling was introduced by Sundaram [5] et al. and in the same paper they have investigated several results on prime cordial labeling.Vaidya and Vihol [6] have also discussed prime cordial labeling in the context of graph operations while in [7] the same authors have discussed prime cordial labeling for some cycle related graphs.Vaidya and Shah [8] have investigated many results on this concept.In the present n .fine To de fo  and are to be dealt se spl K parately and e cordial labeling is shown in Figure 1.
Case 2: In view of the labeling pattern defined above we have 1 (for n odd).Thus we have Hence is a prime cordial graph.ing for and their prime cord l la-ia belling.
In view of pattern defined above we have That is, Let G be the graph is distinct even numbers between 4 and 2n + 2 except 2p with .
In view of the above defined labeling pattern we have . Thus in both the cases we have , we consider following two cases.

Case 2:
is odd, n 5 n    B and its prime cordial labelling.is not a prime cordial graph for n = 3 to n = 7.

Concluding Remarks
As not every graph admit prime cordial labeling it is very interesting to investigate graph or graph famili which admit prime cordial labeling.In this paper we have investigated some new prime cordial graphs.To investigate similar results for other graph fam es as well as in the context of different labeling problems is an open area of research.

3 B are to be 2 d 6
their prime cordial labeling is shown in Figure4.Prime cordial labeling of the graph is shown in Figure5.

3 W
For the gr the possible pairs of labels of adja-

Figure 7
Figure 7. and and th c Figure 8. and its prime cordial labelling.