Some results on (a,d)-distance antimagic labeling




Distance magic graphs, (a, d)-distance antimagic graphs, Circulant graphs, Cartesian and corona product of graphs


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.

Author Biographies

S. K. Patel, Government Engineering College.

Dept. of Mathematics.

Jayesh Vasava, Gujarat University.

Dept. of Mathematics.


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How to Cite

S. K. Patel and J. Vasava, “Some results on (a,d)-distance antimagic labeling”, Proyecciones (Antofagasta, On line), vol. 39, no. 2, pp. 361-381, Apr. 2020.