Total edge Fibonacci - like sequence irregular labeling

In this paper, we define total edge Fibonacci - like sequence irregular labeling $f: V(G) bigcup E(G)$ $ rightarrow {1,2,dots,K}$ of a graph $G=(V,E)$ of vertices and edges of $G$ in such a way that for any two 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-like sequence numbers. The total edge Fibonacci - like sequence irregularity strength, tefls($G$) is defined as the minimum $K$ for which $G$ has a total edge Fibonacci - like sequence irregular labeling. A graph that admits a total edge Fibonacci - like sequence irregular labeling is called a total edge Fibonacci - like sequence irregular graph. In this paper, we prove $P_n$ and $C_n$ and Book (with 3 and 4 sides) are total edge Fibonacci - like sequence irregular graphs.