Odd Fibonacci edge irregular labelling for some simple graphs

Abstract

Let G be a graph with p vertices and q edges and  be an injective function, where k is a positive integer. If the induced edge labeling  defined by f*(uv) = f(u)+f(v), for each , is  a bijection, then the labeling f is called an odd Fibonacci edge irregular labeling of G. A graph which admits an odd Fibonacci edge irregular labeling is called an odd Fibonacci edge irregular graph. The odd Fibonacci edge irregularity strength ofes(G) is the minimum k for which G admits an odd Fibonacci edge irregular labeling. The odd Fibonacci edge irregularity strength for P_n ,  K_1,n , P_nʘK₁, B(m,n) and the non existence of an odd Fibonacci edge irregular labeling for the graphs K_p , K_m,n  have been determined.