Abstract
We analyze the necessary existence conditions for (a, d)-distance antimagic labeling of a graph G = (V, E) of order n. We obtain theorems that expand the family of not (a, d) -distance antimagic graphs. In particular, we prove that the crown Pn ? P1 does not admit an (a, 1)-distance antimagic labeling for n ? 2 if a ? 2. We determine the values of a at which path Pn can be an (a, 1)-distance antimagic graph. Among regular graphs, we investigate the case of a circulant graph.
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