Distance antimagic labeling of join and corona of two graphs
Adarsh Kumar Handa, Aloysius Godinho, Thounaojam Umeshkanta Singh, S. Arumugam ยท AKCE International Journal of Graphs and Combinatorics ยท 2017
Let ๐บ be a graph of order ๐. Let ๐:๐โก(๐บ)โถ{1,2,โฆ,๐} be a bijection. The weight ๐ค๐โก(๐ฃ) of a vertex ๐ฃ with respect to ๐ is defined by ๐ค๐โก(๐ฃ)=โ๐ฅโ๐โก(๐ฃ)๐โก(๐ฅ), where ๐โก(๐ฃ) is the open neighborhood of ๐ฃ. The labeling ๐ is said to be distance antimagic if ๐ค๐โก(๐ข)โ ๐ค๐โก(๐ฃ) for every pair of distinct vertices ๐ข,๐ฃ โ๐โก(๐บ). If the graph ๐บ admits such a labeling, then ๐บ is said to be a distance antimagic graph. In this paper we investigate the existence of distance antimagic labelings of ๐บ+๐ป and ๐บโ๐ป.