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,

k.rajesh3429@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 <F1nΔF2n >, open star of Swastik graphs S(t.Swn) 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 Harary2. 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 Gallian1. Lourdusamy and Patrick4 introduced the concept of sum divisor cordial labeling. Sugumaran and Rajesh6 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 Rajesh7 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 , <F1nΔF2n >, open star of Swastik graph S(t.Swn), when t is odd.





3. CONCLUSION

In this paper, we have proved that the graphs Hn ( n is odd), C3 @ K1,n , <F1nΔF2n > , open star of swastik graph (St.Swn), where t is odd, are sum divisor cordial graphs.

REFERENCES

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  2. F.Harary, Graph Theory, Addison-Wesley, Reading, Massachusetts (1972).
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  6. A.Sugumaran and K.Rajesh, Some new results on sum divisor cordial graphs, Annals of Pure and Applied Mathematics, 14 (1) 45-52 (2017).
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