### Further Results on Sum Divisor Cordial Labeling

**A. Sugumaran and K. Rajesh**

Department of Mathematics,
Government Arts College, Tiruvannamalai-606603, Tamilnadu, INDIA.

email: sugumaranaruna@gmail.com,

(Received on: December 20, 2017)

**ABSTRACT**

A sum divisor cordial labeling of a graph G with vertex set V is a bijection f from V to {1, 2,...,|V (G) |} such that each edge uv assigned the label 1 if 2 divides f (u) + f (v) and 0 otherwise. Further, the number of edges labeled with
0and the number of edges labeled with 1 differ by at most 1. A graph with a sum divisor cordial labeling is called a sum divisor cordial graph. In this paper, we prove that Hn ( n is odd), C3 @ K1,n <F^{1}_{n}ΔF^{2}_{n} >, open star of Swastik graphs S(t.Sw_{n}) when t is odd, are sum divisor cordial graphs.

**AMS Mathematics Subject Classification(2010):**05C78.

**Keywords:**Coloring, Star-in-coloring, Star-in-chromatic number.

**1.INTRODUCTION**

By a graph, we mean a finite undirected graph without loops or multiple edges. For standard terminology and notations related to graph theory, we refer to Harary^{2}. A labeling of graph is a map that carries the graph elements to the set of numbers, usually to the set of non - negative or positive integers. If the domain is the set of edges, then we speak about edge labeling. If the labels are assigned to both vertices and edges, then the labeling is called total labeling. Cordial labeling is extended to divisor cordial labeling, prime cordial labeling, total cordial labeling, Fibonacci cordial labeling etc.

Varatharajan et al.^{9} introduced the concept of divisor cordial labeling. For dynamic survey of various graph labeling, we refer to Gallian^{1}. Lourdusamy and Patrick^{4} introduced the concept of sum divisor cordial labeling. Sugumaran and Rajesh^{6} proved that Swastik graph Swn , path union of finite copies of Swastik graph Swn , cycle of k copies of Swastik graph Swn ( k is odd ), Jelly fish J (n, n) and Petersen graph are sum divisor cordial graphs.
Sugumaran and Rajesh^{7} proved that the Theta graph and some graph operations in Theta graph are sum divisor cordial graphs. Sugumaran and Rajesh8 proved that the Herschel graph and some graph operations in Herschel graph are sum divisor cordial graphs. In this paper we investigate the sum divisor cordial labeling on the graphs such as Hn ( n is odd), C3 @ K1,n ,
<F^{1}_{n}ΔF^{2}_{n} >, open star of Swastik graph S(t.Sw_{n}), when t is odd.

** 3. CONCLUSION**

In this paper, we have proved that the graphs Hn ( n is odd), C3 @ K1,n , <F^{1}_{n}ΔF^{2}_{n} > , open star of swastik graph (St.Sw_{n}), where t is odd, are sum divisor cordial graphs.

**REFERENCES**

- J.A.Gallian, A dynamic survey of graph labeling,
*Electronics Journal of Combinatorics*, (2016). - F.Harary, Graph Theory, Addison-Wesley, Reading, Massachusetts (1972).
- V.J.Kaneria and H.M.Makadia, Some results on graceful labeling for families of plus
graph,
*International Journal of Current Research in Science and Technology*, 1 (4) 17- 23 (2015). - A.Lourdusamy and F.Patrick, Sum divisor cordial graphs,
*Proyecciones Journal of Mathematics*, 35 (1) 115-132 (2016). - A.Nellai Murugan and R.Maria Irudhaya Aspin Chitra, Lucky edge labeling of H-graph,
*A Multi-Disciplinary Refereed Journal*, 8 75-85 (2015). - A.Sugumaran and K.Rajesh, Some new results on sum divisor cordial graphs,
*Annals of Pure and Applied Mathematics*, 14 (1) 45-52 (2017). - A.Sugumaran and K.Rajesh, Sum divisor cordial labeling of Theta graph,
*Annals of Pure and Applied Mathematics*, 14 (2) 313-320 (2017). - A.Sugumaran and K.Rajesh, Sum divisor cordial labeling of Herschel graph,
*Annals of Pure and Applied Mathematics*, 14 (3) 465-472 (2017). - R.Varatharajan, S.Navaneethakrishnan and K.Nagarajan, Divisor cordial graph,
*International J.Math.combin*.4 15-25 (2011).