.svg){kind=logo}
STRONGLY ODD PRIME LABELING OF SOME PATH RELATED GRAPHS
Keywords:
prime labeling, odd prime labeling, strongly prime labeling, strongly odd prime labeling.DOI:
https://doi.org/10.17654/0974165822025Abstract
In this paper, we introduce a new labeling called strongly odd prime labeling. A graph $G$ with vertex set $V(G)$ is said to have an odd prime labeling if there exists an injective function
$$
f: V(G) \rightarrow\{1,3,5, \ldots,|V(G)|\}
$$
such that for every edge $x y \in E(G), f(x)$ and $f(y)$ are relatively prime. A graph $G$ that admits an odd prime labeling is called an odd prime graph and a graph is said to be strongly odd prime graph if for each vertex $v$ of $G$, there exists an odd prime labeling, $f$ satisfying $f(v)=1$. In the present work, we investigate some results for strongly odd primality of some path related graphs.
Received: March 14, 2022
Accepted: April 30, 2022
References
J. A. Bondy and U. S. Murthy, Graph theory, First ed., Springer, 2000.
D. M. Burton, Elementary Number Theory, 6th ed., 2007.
J. A. Gallian, A dynamic survey of graph labeling, Electronic Journal of Combinatorics 17 (2014), DS6.
S. Meena and A. Ezhil, Total prime labeling of some graphs, International Journal of Research in Advent Technology 7(1) (2019), 115-123.
Maged Zakaria Youssef and Zainab Saad Almoreed, On odd prime labeling of graphs, Open Journal of Discrete Applied Mathematics 3(3) (2020), 33-40.
I. Niven, H. S. Zuckerman and H. L. Montgomery, An Introduction to the Theory of Numbers, John Wiley and Sons, 1991.
U. M. Prajapati and K. P. Shah, On odd prime labeling, International Journal of Research and Analytical Reviews 5(4) (2018), 284-294.
U. M. Prajapati and K. P. Shah, Odd prime labeling of graphs with duplication of graph elements, Journal of Applied Science and Computations 5(12) (2018), 1281 1288.
A. Tout, A. N. Dabboucy and K. Howalla, Prime labeling of graphs, National Academy Science Letters 11 (1982), 365-368.
S. K. Vaidya and U. M. Prajapati, Prime labeling in the context of duplication of graph elements, International Journal of Mathematics and Soft Computing 3(1) (2013), 13-20.
Downloads
Published
Issue
Section
License
Copyright (c) 2022 PUSHPA PUBLISHING HOUSE, PRAYAGRAJ, INDIA
This work is licensed under a Creative Commons Attribution 4.0 International License.
_________________________
Attribution: Credit Pushpa Publishing House as the original publisher, including title and author(s) if applicable.
Contact Pushpa Publishing House for more info or permissions.
Journal Impact Factor: 
