Let t be a positive integer and S a set of integers.If for any two elements a and b of S, |a-b| ≥ t, then S is said to be t-separated.For two sets I and J of integers, the distance between I and J, denoted by d(I, J), is defined as min{|i-j|: i ∈ I,j ∈ J}.Let n,t be two positive integers and j1,j2,… ,jm be m nonnegative integers.An n-fold t-separated L(j1,j2,… ,jm)-labeling of a graph G is an assignment f of sets of nonnegative integers of order n to the vertices of G such that the following two conditions are satisfied: (1) for any vertex v, f(v) is t-separated; (2) for any two vertices u and v,if dG(u, v) =i (i ∈ {1, 2,…, m}), then d(f(u)-f(v)) ≥ ji, where dG(u, v) is the length (number of edges) of a shortest path between u and v in G.Integers assigned to vertices by f are called labels.The difference between the maximum and minimum labels used by f is called the span of f.The n-fold t-separated L(j1,j2,… ,jm)-labeling number of G, denoted by λnt(j1,j2,… ,jm)(G), is defined as the minimum span over all n-fold t-separated L(j1, j2,…, jm)-labelings of G.