Graceful Chromatic Number of Unicyclic Graphs

Abstract

We consider that all graph in this paper are finite, simple and connected graph. A graceful k−coloring of a graph is a proper vertex coloring f : V(G) → {1, 2, ..., k}, where k ≥ 2 which induces a proper edge coloring f' : E(G) → {1, 2, ..., k − 1} defined by f' (uv) = |f(u) − f(v)|. A vertex coloring f of graph is a graceful coloring if f is a graceful k−coloring for k ≥ 2. The minimum k for which a graph G has a graceful k−coloring is called a graceful chromatic number of a graph G, denoted by χg(G). In our paper, we will investigate the establish exact value of graceful chromatic number of unicyclic graph namely (m, n)−tadpole graph, n−pan graph and sun graphs