On graceful chromatic number of some graphs
Muhammad Lutfi Asy’ari, Dafik Dafik, Ika Hesti Agustin, Rosanita Nisviasari, Robiatul Adawiyah · Journal of Physics Conference Series · 2022
Abstract We examine that all graphs in this paper are limited, simple and connected. A graceful k-coloring of a graph is a proper vertex coloring f 1 : V (G) → {1, 2,…, k} where k ≥ 2 which induces a proper edge coloring f 2 : E (G) → {1, 2,…, k − 1} characterized by f 2(uυ) = |f 1(u) — f 2 (υ)|. Nethermost k for which a graph G has a graceful k-coloring is named a graceful chromatic number of a graph G, denoted by χg (G). In our research, we will obtain the exact value of the graceful chromatic number of some graphs.