Gaussian Tribonacci R-Graceful Labeling of Some Tree Related Graphs

Abstract

Let r be any natural number. An injective function , where  is the Gaussian Tribonacci number in the Gaussian Tribonacci sequence is said to be Gaussian Tribonacci r-graceful labeling if the induced edge labeling such that  is bijective. If a graph G admits Gaussian Tribonacci r-graceful labeling, then G is called a Gaussian Tribonacci r-graceful graph. A graph G is said to be Gaussian Tribonacci arbitrarily graceful if it is Gaussian Tribonacci r-graceful for all r. In this paper we investigate the Path graph , the Comb graph , the Coconut tree graph the regular caterpillar graph , the Bistar graph  and the Subdivision of Bistar graph are Gaussian Tribonacci arbitrarily graceful.