# MEAN SUM SQUARE PRIME LABELING OF SOME CYCLE RELATED GRAPHS

## Authors

• Sunoj B S Department of Mathematics, Government Polytechnic College, Attingal, Kerala, India
• Mathew Varkey T K Department of Mathematics, T K M College of Engineering, Kollam, Kerala, India

## Keywords:

Graph Labeling, Sum Square, Greatest Common Incidence Number, Prime Labeling, Cycles

## Abstract

Mean sum square prime labeling of a graph is the labeling of the vertices with {0,1,2---,p-1} and the edges with mean of the square of the sum of the labels of the incident vertices or mean of the square of the sum of the labels of the incident vertices and one, depending on the sum is even or odd. The greatest common incidence number of a vertex (gcin) of degree greater than one is defined as the greatest common divisor of the labels of the incident edges. If the gcin of each vertex of degree greater than one is one, then the graph admits mean sum square prime labeling. Here we identify some cycle related graphs for mean sum square prime labeling.

## References

Apostol. Tom M, Introduction to Analytic Number Theory, Narosa, (1998).

Joseph A Gallian, A Dynamic Survey of Graph Labeling, The Electronic Journal of Combinatorics(2016), #DS6, pp 1 – 408.

T K Mathew Varkey, Some Graph Theoretic Generations Associated with Graph Labeling, PhD Thesis, University of Kerala 2000.

Sunoj B S, Mathew Varkey T K, Sum Square Prime Labeling of Some Cycle Related Graphs, International Journal of Informative & Futuristic Research, Vol.4, Issue 10, pp 7846-7851.

Sunoj B S, Mathew Varkey T K, Sum Square Prime Labeling of Some Path Related Graphs, International Journal of Research in Engineering and Applied Sciences,Vol.7, Issue 6, pp 58-62

Sunoj B S, Mathew Varkey T K, Sum Square Prime Labeling of Some Tree Graphs, International Journal of Recent Scientific Research, Vol.8, Issue 6, pp 17447-17449

Sunoj B S, Mathew Varkey T K, Sum Square Prime Labeling of Some Snake Graphs, International Research Journal of Human Resources and Social Sciences, Vol.4, Issue 6, pp 313- 319.

Sunoj B S, Mathew Varkey T K, A Note on Sum Square Prime Labeling, Journal of Emerging Technologies and Innovative Research, Vol.4, Issue 9, pp 213-218.

2017-12-31

## How to Cite

B S, S., & Varkey T K, M. (2017). MEAN SUM SQUARE PRIME LABELING OF SOME CYCLE RELATED GRAPHS . International Journal of Engineering Technologies and Management Research, 4(12), 21–27. https://doi.org/10.29121/ijetmr.v4.i12.2017.131

## Section

Articles  