The concept of [r,s,t]-colourings was introduced by A. Kemnitz and M. Marangio in 2007 as follows: Let G = (V(G), E(G)) be a graph with vertex setV(G) and E(G) Given non-negative integers r, s and t, an [r, s, t]-colouring of a graph G = ( V(G), E(G)) is a mapping C from V(G) ∪ E(C) to the colour set {0, 1,2, ...,k-1 } such that |c(v_i)-c(v_i)|≥r for every two adjacent vertices v_i, v_j , |c(e_i) - c(e_j) |≥ for every two adjacent edges e_i, e_j, and |c(v_i)-c(e_j)|≥t for all pairs of incident vertices and edges, respectively. The [r, s, t]-chromatic number x_(r,s,t)(G) of G is defined to be the minimum k such that G admits an [r, s, t]-colouring. In this paper, we determine the [r, s, t]-chromatic number for join graphs S_n +O_m.
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