Graceful Chromatic Number of Unicyclic Graphs
Ridho Alfarisi, Dafik Dafik, Rafiantika Megahnia Prihandini, Robiatul Adawiyah, Ermita Rizki Albirri, Ika Hesti Agustin · Journal of Physics Conference Series · 2019
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 χ g ( 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