Distance antimagic labelings of product graphs

Risma Yulina Wulandari (Institut Teknologi Bandung)
Rinovia Simanjuntak (Institut Teknologi Bandung)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 11, No 1 (2023): Electronic Journal of Graph Theory and Applications

A graph G is distance antimagic if there is a bijection f : V(G)→{1, 2, …, |V(G)|} such that for every pair of distinct vertices x and y applies w(x)≠w(y), where w(x)=Σ z ∈ N(x)f(z) and N(x) is the neighbourhood of x, i.e., the set of all vertices adjacent to x. It was conjectured that a graph is distance antimagic if and only if each vertex in the graph has a distinct neighbourhood. In this paper, we study the truth of the conjecture by posing sufficient conditions and constructing distance antimagic product graphs; the products under consideration are join, corona, and Cartesian.