Some New Odd prime Graphs

Meena S, Gajalakshmiy G

Abstract


For a graph G, a bijection f is called an odd prime labeling , if f
from V to f1; 3; 5; ::::; 2jV j - 1g for each edge uv in G the greatest
common divisor of the labels of end vertices (f(u); f(v)) is one. In
this paper we investigate the existence of odd prime labeling of some
new classes of graphs and we prove that the graphs such as the Z -Pn
graph, Fish graph, Umbrella graph, Cocount tree , F-tree, Y -tree and
Double Sunflower graph are odd prime graphs.

Keywords


Odd prime graph, Z − Pn graph, Fish graph, Umbrella graph,Cocount tree , F-tree, Y -tree, Double Sunflower graph.

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References


T. Deretsky, S. Lee, and J. Mitchem. On vertex prime labelings of graphs, in

graph theory, combinatorics and applications, j. alavi, g. chartrand, o. oellerman, and a. schwenk, eds.,. Proceedings 6th International Conference Theory

and Applications of Graphs (Wiley, New York),, 1:359 – 369, 1991.

J. Gallian. A dynamic survey of graph labeling. DS6, 2009.

J .A.Bondy and U .S. R.Murthy. Graph Theory and Applications. (NorthHolland), New York, 1976.

S. Meena and P. Kavitha. Prime labeling of duplication of some star related

graphs. International Journal of Mathematics Trends and Technology, 23:26

– 32, 2015.

S. Meena and J. Naveen. On prime vertex labeling of corona product of bicyclic

graphs. Journal of Computer and Mathematical Sciences, 9:1512 – 1526, 2018.

S. Meena and K. Vaithilingam. Prime labeling for some crown related graphs.

International Journal of Scientific & Technology Research, 2:92 – 95, 2013.

S. Meena, P. Kavitha, and G. Gajalakshmi. Prime labeling of h super subdivision

of cycle related graph. AIP Conference Proceedings (communicated).

S. Meena, G. Gajalakshmi, and P. Kavitha. Odd prime labeling for some new

classes of graph (communicated). SEAJM, 2021.

U. Prajapati and K. Shah. On odd prime labeling. International journal of Research and Analytical Reviews, 5:284 – 294, 2018.

A. Tout, A. Dabboucy, and K. Howalla. Prime labeling of graphs. Nat. Acad. Sci

letters, 11:365 – 368, 1982.

S. Vaidya and K. Kanani. Prime labeling for some cycle related graphs. Journal

of Mathematics Research, 2:98 – 104, 2010




DOI: http://dx.doi.org/10.23755/rm.v46i0.1057

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