### Totally magic d-lucky number of 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.

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DOI: http://dx.doi.org/10.23755/rm.v44i0.920

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