Distance Antimagic Labeling of Special Classes of Graphs

Labeled graphs serve as a versatile mathematical model with diverse applications in engineering fields. A bijective function 𝜗:𝑉(𝐺) → {1,2,…,𝑛} is a distance antimagic labeling of a graph G with n vertices such that the vertex weights determined by 𝜔(𝑎) = ∑ 𝑏𝜖𝑁(𝑎) 𝜗(𝑏) Are unique i.e. 𝜔(𝑎) ≠ 𝜔(𝑏) for distinct vertices 𝑎,𝑏 𝜖 𝑉(𝐺) where N(a) is the open neighbourhood of vertex a in G. This paper demonstrates that distance antimagic labeling and inclusive distance antimagic labeling exist for certain special graph constructions- specifically Mycielskian graphs, splitting graphs, and shadow graphs when applied to fundamental graph classes like cycles, paths, crown graph and star graphs. Furthermore, the uniqueness of the calculated vertex weights is confirmed through a Python-Based Computational Algorithm.