Total Neighborhood Prime Labeling of Cycle Related Graphs

Rajesh Kumar T.J.

doi:https://doi.org/10.14445/22315373/IJMTT-V66I1P513

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 66 | Issue 1 | Year 2020 | Article Id. IJMTT-V66I1P513 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I1P513

Total Neighborhood Prime Labeling of Cycle Related Graphs

Rajesh Kumar T.J.

Citation :

Rajesh Kumar T.J., "Total Neighborhood Prime Labeling of Cycle Related Graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 1, pp. 103-109, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I1P513

Abstract

Let G = (V,E) be a graph with p vertices and q edges. A bijection f: V(G) U E(G) -> { 1,2,3,....,p+q } is said to be total neighborhood prime labeling if it satisfies that for each vertex of degree at least two ,the gcd of labeling on the neighborhood vertices is one and for each vertex of degree at least two, the gcd of labeling on the induced edges is one. In this paper we investigate total neighborhood prime labeling of cycle Cn with a chord, switching of any vertex in a cycle cn, path union of finite number of copies of the cycle and the graph obtained by joining two copies of a cycle Cn by a path Pk

Keywords

Neighborhood prime labeling, total neighborhood prime labeling, vertex switching, path union

References

[1] Tout, A. N. Dabboucy, K. Howalla, “Prime labeling of graphs”, Nat. Acad. Sci. Letters, 11 (1982), 365-368.
[2] S. K. Patel, N. P. Shrimali,” Neighborhood-prime labeling” , International Journal of Mathematics and Soft Computing, 5, No. 2. (2015), 135-143.
[3] Rajesh Kumar T.J., Mathew Varkey T.K., “A note on Total neighborhood prime labeling”, International journal of Mathematics Combinatorics, 4 (2018).
[4] N.P.Shrimali,Parul B. Pandya, “ Total Neighborhood Prime Labeling of Some Graphs”,International Journal of Scientific Researc h in Mathematical and Statistical Sciences,5,Issue 6,pp.157-163,Dec 2018
[5] J. Gross, J. Yellen, “Graph theory and its applications”, CRC press, (1999).
[6] J.A.Gallian, “A dynamic survey of graph labeling”, The Electronic Journal of Combinatorics (2017), # DS6.
[7] David M. Burton, Elementary Number Theory, Sixth Edition, Tata MacGraw Hill, India, 2012.
[8] Mathew VarkeyT.K.,Rajesh Kumar T.J.,”A Note on Neighbourhood PrimeLabeling”,International Journal of Math.Combin.4,pp.161-167,2016.