1. Introduction
Consider a simple finite graph. Terms and terminologies have been
referred from the book [1]. A graph G’ with graceful labeling is
given by a function g. It contains an edge with injective function g
assigned from V(G’) to {0,1,2,…,r}. When all the edges ‘ab’ is
reserved to be the edge label |g(a)− g(b)|, at that
point the subsequent edge names are particular. The graceful labeling
accepted by a graph is known as a graceful graph. Some classes of trees
using graceful labeling were studied by A. Rosa 1966 [2]-paths and
caterpillars, G. Sethuraman et al 2009 [3]-attaching caterpillars
with other caterpillars, I. Cahit 2002 [4]-canonic labeling
technique, R.E. Aldred et al 1998 [5] -lobsters, Jesintha et al 2011
[6]- constructed certain infinite families of graceful Acharya 1982
[7], A. Gallian 2019 [8]-surveyed on graceful tree conjecture
[9-22]. A star graph can be defined as the complete bipartite graph
𝐾1,r containing r + 1 vertices and r edges. A simple
graph can be defined as a graph that does not contain a self-loop or
parallel edges. A path 𝑃𝑛 is acquired by signing up for
𝑢𝑖 to the consecutive vertices 𝑢𝑖+1 for
1 ≤ 𝑖 ≤ 𝑛 − 1.
In mathematical models, In a wide variety of mathematical models,
Labeled graphs have played a remarkable usage. In the application of
designing X-Ray crystallography, formulating an addressing system using
a communication network, determining the layouts of a perfect circuit,
problems based on the addition of numbers, etc. are used.