TOTAL EDGE FIBONACCI IRREGULAR LABELING OF SOME STAR GRAPHS

A total edge Fibonacci irregular labeling $f: V(G) cup E(G) rightarrow {1,2,dots,K}$ 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 $x^{'}y^{'}$ their weights $f(x)+f(xy)+f(y)$ and $f(x^{'})+f(x^{'}y^{'})+f(y^{'})$ 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 prove $K_{1,n}$, bistar $textless(B_{n,n})textgreater$, subdivision of bistar$textless(B_{n,n};W)textgreater$ and $textless(B_{2,n};W_i)textgreater$ $(1leq ileq n)$ are total edge Fibonacci irregular graphs.