Graceful coloring of ladder graphs

Abstract

A graceful k-coloring of a non-empty graph G = (V, E) is a proper vertex coloring f : V (G) → {1, 2, ..., k}, k ≥ 2, which induces a proper edge coloring f*: E(G) → {1, 2, ..., k − 1} defined by f*(uv) = |f(u) − f(v)|, where u, v ∈ V (G). The minimum k for which G has a graceful k-coloring is called graceful chromatic number, χg(G). The graceful chromatic number for a few variants of ladder graphs are investigated in this article.