Total Edge Fibonacci Irregular Labeling of some Star Graphs

Abstract

A total edge Fibonacci irregular labeling f : V (G) S E(G) → {1, 2, . . . ,K} of a graph G = (V,E) is a labeling of vertices and edges of G in such a way that for any different edges xy and x 0 y 0 their weights f( x ) + f( xy ) + f( y ) and f( x 0 ) + f( x 0 y 0 ) + f( y 0 ) are distinct Fibonacci numbers. The total edge Fibonacci irregularity strength, tefs( G) is defined as the minimum K for which G has a total edge Fibonacci irregular labeling. If a graph has a total edge Fibonacci irregular labeling, then it is called a total edge Fibonacci irregular graph. In this paper, we proved K1,n , Bistar , subdivision of bistar and (1 ≤ i ≤ n) are total edge Fibonacci irregular graphs.