Totally magic d-lucky number of graphs

N Mohamed Rilwan, A Nilofer


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.


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

Full Text:



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.



  • There are currently no refbacks.

Copyright (c) 2022 N Mohamed Rilwan, A Nilofer

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Ratio Mathematica - Journal of Mathematics, Statistics, and Applications. ISSN 1592-7415; e-ISSN 2282-8214.