Congruence distance magic graphs

02/11/2023

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by   Himadri Mukherjee, et al.

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In this paper, we introduce a series of necessary conditions namely the concept of p-distance magic labeling and give a relation between labeling and graph-theoretic properties of a graph. We also prove that a graph which is p-distance magic, for all p is also distance magic. As a result we have a new necessary and sufficient condition for a distance magic graph. We also obtain conditions for when the “group distance magic constant will be unique".