T-coloring

Summary

In graph theory, a T-Coloring of a graph $G = (V, E)$, given the set T of nonnegative integers containing 0, is a function $c: V(G) \to \mathbb{N}$ that maps each vertex to a positive integer (color) such that if u and w are adjacent then $|c(u) - c(w)| \notin T$. In simple words, the absolute value of the difference between two colors of adjacent vertices must not belong to fixed set T. The concept was introduced by William K. Hale. If T = $\{0\}$ it reduces to common vertex coloring.