Vertex k-Prime Labeling of Cyclic Snakes

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DOI:

https://doi.org/10.26713/cma.v14i1.1989

Keywords:

Vertex k-prime labeling, Triangular snakes, Pentagonal snakes, Cyclic snakes, Corona graphs

Abstract

For each positive integer k, a simple graph G of order p is said to be k-prime labeling if there exists an injective function f whose labels are from k to k+p−1 that induces a function f+:E(G)→N of the edges of G defined by f+(uv)=gcd(f(u),f(v)), ∀ e=uv∈E(G) such that every pair of neighbouring vertices are relatively prime. This type of graph is known as a k-prime graph. In this paper, we redefine the labeling as vertex k-prime labeling for some k positive integers and study some cyclic snake graphs and corona graphs of the form mCn⊙K1 which admit vertex $k$-prime labeling.

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References

S. T. Arockiamary and G. Vijayalakshmi, k-Prime labeling of one point union of path graph, Procedia Computer Science 172 (2020), 649 – 654, DOI: 10.1016/j.procs.2020.05.084.

C. Barrientos, Graceful labelings of cyclic snakes, Ars Combinatoria 60 (2001), 85 – 96, URL: http://www.combinatoire.ca/ArsCombinatoria/Vol60.html.

R. Frucht and F. Harary, On the corona of two graphs, Aequationes Mathematicae 4 (1970), 322 – 325, DOI: 10.1007/BF01844162.

J. A. Gallian, A dynamic survey of graph labeling, Electronic Journal of Combinatorics DS6 (2021), Version 24, 576 page, URL: https://www.combinatorics.org/files/Surveys/ds6/ds6v24-2021.pdf.

S. Vaidya and U. Prajapati, Some results on prime and k-prime labeling, Journal of Mathematics Research 3(1) (2011), 66 – 75, DOI: 10.5539/jmr.v3n1p66.

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Published

09-05-2023
CITATION

How to Cite

Arockiamary, S. T., & Vijayalakshmi, G. (2023). Vertex k-Prime Labeling of Cyclic Snakes. Communications in Mathematics and Applications, 14(1), 9–20. https://doi.org/10.26713/cma.v14i1.1989

Issue

Vol. 14 No. 1 (2023)

Section

Research Article

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