A new graph labeling with Tribonacci, Fibonacci and Triangular numbers

In this paper, a new graph labeling technique using three sequences of numbers, namely Tribonacci, Fibonacci and Triangular is introduced. They are named as Tribo-Fibo-Triangular labeling and denoted as TF \(\Delta \) $\mathrm{\Delta }$ labeling. Assignment of the labeling is done based on the families of generalized Petersen graphs GP (n,2), GP(n,3) and a generalization of these graph are also presented. Applications related to recruitment of employees in a health care sector and the selection of teams in a school ambience are arrived by using of these three sequences of graphs along with computational intelligence. A board game is developed and presented using these three sequences.