An observation on vertex sum cube labeling for comb and K_1m @ K_1n graphs

In this paper, the new concept vertex sum cube labeling has been introduced and a formula for vertex sum cube labeling has been established. A function θ is called a Vertex sum cube labeling of a graph G with edges, if the vertices of G to the set {0,1,2, p - 1} such that when each edge is assigned the label θ(uv)= u³ + v³ + 3u²v + 3uv², then the resulting edge labels are distinct cube numbers. In this paper, some families of graphs such as Comb K_1m @ K_1n and has been investigated.