Indian Journal of Science and Technology

Abstract

Objective: To identify a new family of Lucas antimagic graph. Methods: A (p;q) graph G is said to be a Lucas antimagic graph if there exists a bijection f : E(G) ! fL1;L2;


Lqg such that the induced injective function f  : V(G) ! f1;2; : : :åLqg given by f  (u) = åe2E(u) f (e) are all distinct (where E(u) is the set of edges incident to u). Findings: In this paper the Lucas Antimagic Labeling of Subdivision of star, Shadow graph of star, Splitting graph of star, Subdivision of Bistar, Shadow graph of Bistar, Splitting graph of Bistar are found. Novelty: It involves the mathematical formulation for labeling the edges of a given graph which in turn gives rise to a new type of labeling called the Lucas antimagic labeling.

Keywords: Subdivision graph; Shadow graph; Splitting graph; Star; Bistar