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

Author
Patel, S. K.

Vasava, Jayesh

Full text
https://www.revistaproyecciones.cl/article/view/3475
10.22199/issn.0717-6279-2020-02-0022
Abstract
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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