Totally magic d-lucky number of graphs

Authors

  • N Mohamed Rilwan Department of Mathematics, Sadakathullah Appa College (Autonomus), Rahmath nagar, Tirnelveli-627011, India
  • A Nilofer Department of Mathematics, Sadakathullah Appa College (Autonomus), Rahmath nagar, Tirunelveli 627011, Affiliated to Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli 627012, India;

DOI:

https://doi.org/10.23755/rm.v44i0.920

Keywords:

Totally magic d-lucky labeling, totally magic d-lucky number, zero divisor graphs.

Abstract

In this paper we introduce a new labeling named as, totally magic d-lucky labeling, find the totally magic d-lucky number of some standard graphs like wheel, cycle, bigraph etc. and find the totally magic d-lucky number of some zero divisor graphs. A totally magic d-lucky labeling  of a graph G = (V, E) is a labeling of vertices and label the graph's edges using the total label of its incident vertices in such a way that for any two different incident vertices u and v, their colors ,  are distinct and for any different edges in a graph, their weights    are same Where  represents the degree of u in a graph and  represents the open neighbourhood of u in a graph.

References

Mirka Miller, Indira Rajasingh, D.Ahima Emilet, D.Azubha Jemilet, d-lucky labeling of graphs. Precedia computer science 57(2015) 766-771.

S. Czerwinski, J. Grytczuk, V. Zelazny, lucky labeling of graphs. Information Processing letters,109 (2009) 1078-1081.

A. D. Garciano, RM Marcelo, MJP Ruiz and MAC Tolentino, on the sigma chromatic number of the zero divisor graphs of the ring of integers modulo. Journal of physics, Conf. Series 1836(2021) 012013, IOP Publishing.

Anderson DF and Livingston PS 1999, Journal of Algebra, 217 (434-447).

G. Exoo, A. Ling, J. Mcsoriey, N. Philips, and W. Wallis, totally magic graphs. Discrete Mathematics, 254 (2002) 103-113.

Sarifa Khatun, Graceful labeling of some zero divisor graphs. Electronic Notes in Discrete Mathematics 63(2017), 189-196.

I. Cahit, Some totally modular cordial graphs. Discussiones Mathematicae Graph theory 22 (2002), 247-258.

Downloads

Published

2022-12-11

Issue

Vol. 44 (2022): Special Issue: Recent Trends in Mathematics and its Applications

Section

Volume 45-2023

License

This journal provides immediate open access to its content on the principle that making research freely available to the public supports a greater global exchange of knowledge. The journal is committed to real and immediate open access for academic work. All of the journal articles are free to access immediately from the date of publication. There are no charge for readers to download articles and reviews for their own scholarly use. Benefits of open access for authors, include:

  • Free access for all users worldwide
  • Increased visibility and readership
  • Rapid publication
  • No spatial constraints
  • Authors can share their research papers on their personal web-pages (i.e. ResearchGate, etc.)

Ratio Mathematica publishes open access articles under the terms of the Creative Commons Attribution (CC BY) License. The Creative Commons Attribution License (CC-BY) allows users to copy, distribute and transmit an article, adapt the article and make commercial use of the article. The CC BY license permits commercial and non-commercial re-use of an open access article, as long as the author is properly attributed. Copyright on any research article published by Ratio Mathematica is retained by the author(s). Authors grant Ratio Mathematica a license to publish the article and identify itself as the original publisher. Authors also grant any third party the right to use the article freely as long as its original authors, citation details and publisher are identified. 
For further information visit: https://creativecommons.org/licenses/by/3.0/. The following logo will appear in any paper that will be published from the volume number 31/2016 onwards.