Home / Current Issue / Paper 1702334
Consecutive Cyclic k - Prime Labeling of a Ladder Graphand its application to Crab graph
Subject area: Science,Engineering and Technology · Area of research: Mathematics
Abstract
A graph G order n is said to have a k?prime labeling, wherek is a positive integer, if the vertices can be labeled with positive integers from k to k+|n|-1 such that each pair of adjacent vertices are relatively prime. In this work, a consecutive cyclic k ? prime labeling for ladder graphs is given under certain conditions. Furthermore, a new graph called Crab graph is introduced and a prime labeling is discussed for it.
Keywords
Crab Graph, Ladder Graph, k-prime labeling, prime labeling
References
[1] S. T. Arockiamary, G. Vijayalakshmi, -Prime labeling of certain cycle connected graphs,| Malaya Journal of Matematik, vol. S, no. 1, pp. 280-283, 2019.
[2] A. H. Berliner, N. Dean, J. Hook, A. Marr, A. Mbirika, and C. D. McBee, Coprime and prime labeling of graphs,| Journal of Integer Sequences, vol. 19, no. 2, 2016.
[3] J. A. Gallian, A Dynamic Survey of Graph Labeling, The Electronic Journal of Combinatorics,| vol. 16, no. 6, pp. 1-219, 2009.
[4] R. Tout, A. N. Dabbouchy, K. Howalla, Prime labeling of graphs,| national Academy of Science Letters-India, vol. 5, no. 11, pp. 365-368, 1982.
[5] T.R.D.S.M. Thennakoon, M.D.M.C.P. Weerarathna and A.A.I. Perera, Prime Labeling of NewlyConstructed Graph Using Star Graphs and Complete Bipartite Graphs,|Sumerianz Journal ofScientific Research, vol. 3, no. 2, pp. 10-17, 2020.
[6] S. K. Vaidya, and U. M. Prajapati, Some Results on Prime and -Prime Labeling,| Journal of Mathematics Research, vol. 3, no. 1, February 2011.
How to cite this paper
@article{1702334,
author = {M. D. M. C. P. Weerarathna, D. M. T. B. Dissanayake, W. V. Nishadi, K.D.E. Dhananjaya, T. R. D. S. M. Thennakoon; A. A. I. Perera},
title = {Consecutive Cyclic k - Prime Labeling of a Ladder Graphand its application to Crab graph},
journal = {Iconic Research And Engineering Journals},
year = {2020},
volume = {3},
number = {11},
pages = {278-283},
issn = {2456-8880},
url = {https://www.irejournals.com/formatedpaper/1702334.pdf},
abstract = {A graph G order n is said to have a k?prime labeling, wherek is a positive integer, if the vertices can be labeled with positive integers from k to k+|n|-1 such that each pair of adjacent vertices are relatively prime. In this work, a consecutive cyclic k ? prime labeling for ladder graphs is given under certain conditions. Furthermore, a new graph called Crab graph is introduced and a prime labeling is discussed for it.},
keywords = {Crab Graph, Ladder Graph, k-prime labeling, prime labeling},
month = {May},
}