[r, s, t]-coloring of the joint graph C m ∨ C n

The coloring of graph has been an important and active branch in graph theory. [r, s, t]-coloring is a generalization of the classical vertex coloring, edge coloring and total coloring of a graph, which has significant applications in the training arrangement of some tournament and the frequency channel assignment and so on. This paper give a study of the [r, s, t]- coloring and the [r, s, t]- chromatic number of the joint graph C m ∨ C n in certain conditions.