Geodesic
Neighborhood-prime labeling of snake graphs
Sanjay Kantibhai Patel1 ; Ankur N. Kansagara2 ; Sanjay Kantibhai Patel ; Ankur N. Kansagara
1Department of Mathematics, Government Engineering College, Bhuj, India
2Department of Mathematics, Gujarat University, Ahmedabad, India
Acta mathematica Universitatis Comenianae, Tome 90 (2021) no. 4, pp. 353-376 
Sanjay Kantibhai Patel; Ankur N. Kansagara; Sanjay Kantibhai Patel; Ankur N. Kansagara. Neighborhood-prime labeling of snake graphs. Acta mathematica Universitatis Comenianae, Tome 90 (2021) no. 4, pp. 353-376. http://geodesic.mathdoc.fr/item/AMUC_2021_90_4_a0/
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     author = {Sanjay Kantibhai Patel and Ankur N. Kansagara and Sanjay Kantibhai Patel and Ankur N. Kansagara},
     title = { Neighborhood-prime labeling of snake graphs},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {353--376},
     year = {2021},
     volume = {90},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2021_90_4_a0/}
}
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Voir la notice de l'article provenant de la source Comenius University

We study neighborhood-prime labeling in the context of snake graphs of the types $C_k^m$ and $C_{k,q}^m$. In particular, we prove that the snake graphs of the type $C_k^m$ are neighborhood-prime if and only if either $k \not\equiv 2\pmod 4$ or $m\not\equiv 1\pmod 4$. Further, we also show that $C_{k,2}^m$ and $C_{k,3}^m$ are neighborhood-prime for all $m \ge 2$.