On graceful chromatic number of some graphs

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 f1: V (G) → {1, 2,..., k} where k ≥ 2 which induces a proper edge coloring f2: E (G) → {1, 2,..., k − 1} characterized by f2 (uv) = |f1 (u) − f2 (v)|. 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.