[r, s, t]-colorings of fans

Given non-negative integers r, s and t, an [r, s, t]-coloring of a graph G = (V (G), E (G)) is a function c from V (G) boolean OR E(G) to the color set {0,1, ..., k - 1} such that vertical bar c(v(z)) - c(v(j))vertical bar >= r for every two adjacent vertices v(i), v(j), vertical bar c(e(i)) - c(e(j))vertical bar >= s for every two adjacent edges e(i), e(j), and vertical bar c(v(i)) - c(e(j))vertical bar >= t for all pairs of incident vertices v(z) and edges e(j). The [r, s, t]-chromatic number (Xr,s,t)(G) is the minimum k such that G admits an [r, s, t]-coloring. In this paper, we examine [r, s, t]-chromatic numbers of fans for every positive integer r, s and t.