Graceful Coloring of Ladder Graphs

Abstract

A graceful k-coloring of a non-empty graph $G=(V,E)$ is a proper vertex coloring $f:V(G)\to \{1,2,...,k\}$, $k\ge 2$, which induces a proper edge coloring $f^{\ast }:E(G)\to \{1,2,...,k-1\}$ defined by $f^{\ast }(uv)=|f(u)-f(v)|$, where $u,v\in V(G)$. The minimum $k$ for which $G$ has a graceful $k$-coloring is called graceful chromatic number, ${\chi }_g(G)$. The graceful chromatic number for a few variants of ladder graphs are investigated in this article.

10 pages, 1 figure