Odd Prime Labeling of Graphs Related to Circular Ladder





Odd prime graph, Circular ladder, Subdivision


In a graph \(G\) with point set \(V\) a mapping $f$ is said to be an odd prime labeling if \(f\) is a one-to-one function from point set \(V\) to \({\{1,3,5,2|V|-1}\}\) satisfying the condition that for each line \(uv\) in \(G\) the greatest common divisor of the labels of the end points \(f(u),f(v)\) is one. Investigated in this paper the odd prime labeling of circular ladder related graphs and we prove that the graphs such as \(CL(n)\), \(SCL(n)\), \(CL(n)\bigodot K_{1}\), \(CL(n)\bigodot \bar{K}_{2}\), \(CL(n) \bigodot\bar{K}_{3}\) are all odd prime graphs.


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J. A. Bondy and U. S. R. Murty, Graph Theory and Applications, North-Holland, New York (1976), URL: https://www.zib.de/groetschel/teaching/WS1314/BondyMurtyGTWA.pdf.

T. Deretsky, S. M. Lee and J. Mitchem, On vertex prime labelings of graphs, in: Graph Combinatorics and Applications, J. Alavi, G. Chartrand, O. Oellerman and A. Schwenk (eds.), Proceedings of the 6th International Conference Theory and Applications of Graphs, Wiley, New York, Vol. 1 (1991), 359 – 369.

H.-L. Fu and K.-C. Huang, On prime labeling, Discrete Mathematics 127 (1994), 181 – 186, URL: https://www.math.nycu.edu.tw/research/DOWNLOAD_FILES/hlfu/34.%20On%20prime%20labeling.pdf.

J. A. Gallian, A dynamic survey of graph labeling, The Electronic Journal of Combinations 16 (2009), DS6, URL: https://www.combinatorics.org/ojs/index.php/eljc/article/view/DS6/pdf.

S. Meena and P. Kavitha, Prime labeling of duplication of some star related graphs, International Journal of Mathematics Trends and Technology 23(1) (2015), 26 – 32, DOI: 10.14445/22315373/IJMTT-V23P504.

S. Meena and K. Vaithilingam, Prime labeling for some crown related graphs, International Journal of Scientific & Technology Research 2(3) (2013), 92 – 95, URL: https://www.ijstr.org/final-print/mar2013/Prime-Labeling-For-Some-Crown-Related-Graphs.pdf.

U. M. Prajapati and K. P. Shah, On odd prime labeling, International Journal of Research and Analytical Reviews 5(4) (2018), 284 – 294, URL: http://ijrar.com/upload_issue/ijrar_issue_20542373.pdf.

A. Tout, A. N. Dabboucy and K. Howalla, Prime labeling of graphs, National Academy Science Letters 11 (1982), 365 – 368.

S. K. Vaidya and K. K. Kanani, Prime labeling for some cycle related graphs, Journal of Mathematics Research 2(2) (2010), 98 – 104, DOI: 10.5539/jmr.v2n2p98.




How to Cite

Meena, S., & Gajalakshmi, G. (2022). Odd Prime Labeling of Graphs Related to Circular Ladder. Communications in Mathematics and Applications, 13(4), 1307–1315. https://doi.org/10.26713/cma.v13i4.2173



Research Article