Graceful Labeling of Chain Graphs with Pendants
W. K. M. Indunil, A. A. I. Perera · Zenodo (CERN European Organization for Nuclear Research) · 2022
Graph labeling is one of the most popular research areas in graph theory. There is a vast amount of literature available on graph labeling. In this research, we especially concentrate on a special type of graph labeling method called vertex graceful labeling. A simple connected graph 𝐺 is said to be a vertex graceful if there exists a vertex graceful labeling on the vertices of 𝐺 starting from 1. Graceful labeling of 𝐺 is a vertex labeling which is defined as an injective mapping from to such that the edge labeling defined by is also injective. There is a very famous open conjecture in this area abbreviated as GTC which stands for graceful tree conjecture or Ringel - Kotzig conjecture which hypothesizes that all trees are graceful. In this research work, we introduce graceful labeling for a chain of the key graph with a finite number of pendants and a chain of linear dice graphs with a finite number of pendants.