One Raised Product Prime Labeling of Some Star Related Graphs

B.S. Sunoj¹ , T.K. Mathew Varkey²

1. Department of Mathematics, Government Polytechnic College, Attingal, Kerala, India.
2. Department of Mathematics, TKM College of Engineering, Kollam, Kerala, India.

Section:Research Paper, Product Type: Isroset-Journal
Vol.5 , Issue.3 , pp.18-23, Jun-2018

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i3.1823

Online published on Jun 30, 2018

Copyright © B.S. Sunoj, T.K. Mathew Varkey . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
One raised product prime labeling of a simple. finite and un direct graph G with p vertices and q edges is the labeling of the vertices of the graph with first p natural numbers, edges with product of the labels of the end vertices plus one. If the greatest common divisor of each vertex of degree greater than one is one then the graph is called one raised product prime graph. Here the greatest common divisor of the labels of the edges incident on a vertex is called greatest common incidence number of that vertex. Here we proved that star, bistar, splitting graph of a star, shadow graph of a star , jelly fish graph and some more star related graphs admit one raised product prime labeling.

Key-Words / Index Term :
Graph labeling, product, prime labeling, prime graphs, star

References :
[1] Apostol. Tom M, Introduction to Analytic Number Theory, Narosa, (1998).
[2] F Harary, Graph Theory, Addison-Wesley,Reading, Mass, (1972
[3] Joseph A Gallian, A Dynamic Survey of Graph Labeling, The Electronic Journal of Combinatorics(2015), #DS6, Pages 1 – 389.
[4] T K Mathew Varkey, Some Graph Theoretic Operations Associated with Graph Labelings, PhD Thesis, University of Kerala 2000.
[5] Sunoj B S, Mathew Varkey T K, “One Raised Product Prime Labeling of Some Cycle Related Graphs ”, Journal of Harmonized Research in Applied Science, Vol.6-No.2, May 2018, pp 49-54.
[6] Sunoj B S, Mathew Varkey T K, “One Raised Product Prime Labeling of Some Snake Graphs ”, International Journal of Research in Advent Technology, Vol.6-No.5, May 2018, pp 455-459.
[7] Sunoj B S, Mathew Varkey T K, “One Raised Product Prime Labeling of Some Path Related Graphs”, Research Guru – Online Journal of Multidisciplinary Subjects, Vol.12-No.1, June 2018, pp 950-959.
[8] Sunoj B S, Mathew Varkey T K, “Hexagonal Difference Prime Labeling of Some Path Graph”, Mapana J Sci., Vol.16, No.3, June 2017, pp 41-46.