Proper d-Lucky Labeling of Rooted Products and Corona Products of Certain Graphs

Abstract

Objectives: To examine rooted products graph and corona product of path graph with itself and cycle graph with itself for the existence of d-lucky labeling. Methods: In this study, d-lucky number for Rooted product graph of path graph to path graph (Pn ◦ Pn) and Corona product graph (Pn⊙ Pn) are computed. Method of construction is used throughout this paper to prove the theorems. Findings: Rooted products and corona products of path with itself and cycle graph with itself admit d-lucky labeling and d-lucky numbers for the same are obtained. Novelty: d-lucky numbers for some graphs are obtained by some authors but for rooted product of path with itself and corona products of path with itself and cycle with itself are new findings. Keywords: Proper Lucky labeling; Rooted product; corona product; d-lucky; d-lucky labeling