Graceful Labeling of Chain Graphs with Pendants

Abstract

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 �� is said to be a vertex graceful if there exists a vertex graceful labeling on the vertices of �� starting from 1. Graceful labeling of �� is a vertex labeling ��, which is defined asan injective mapping from ��(��) to [0, |��(��)|]such that the edge labeling ����: ��(��) →[1, |��(��)| ] 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.