Skolem Difference Mean Graphs

A graph G = (V, E) with p vertices and q edges is said to haveskolem difference mean labeling if it is possible to label the verticesx ∈ V with distinct elements f(x) from 1, 2, 3, · · · , p+q in such a waythat for each edge e = uv, let f *(e) = l|f(u)- 2 f(v)|m and the resultinglabels of the edges are distinct and are from 1, 2, 3, · · · , q. A graphthat admits a skolem difference mean labeling is called a skolem difference mean graph. In this paper, we prove Cn@Pm(n ≥ 3, m ≥ 1),T hK1,n1 : K1,n2 : · · · : K1,nmi, T hK1,n1 ◦ K1,n2 ◦ ◦ ◦ K1,nmi,St(n1, n2, · · · , nm) and Bt(n, n, · · · , n| {z }m times) are skolem difference mean graphs.