Some results on (a,d)-distance antimagic labeling
DOI:
https://doi.org/10.22199/issn.0717-6279-2020-02-0022Keywords:
Distance magic graphs, (a, d)-distance antimagic graphs, Circulant graphs, Cartesian and corona product of graphsAbstract
Let G = (V,E) be a graph of order N and f : V → {1, 2,...,N} be a bijection. For every vertex v of graph G, we define its weight w(v) as the sum ∑u∈N(v) f(u), where N(v) denotes the open neighborhood of v. If the set of all vertex weights forms an arithmetic progression {a, a + d, a + 2d, . . . , a + (N − 1)d}, then f is called an (a, d)-distance antimagic labeling and the graph G is called (a, d)-distance antimagic graph. In this paper we prove the existence or non-existence of (a, d)- distance antimagic labeling of some well-known graphs.
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