A Study on Vertex Sum Cube Labeling for Path and Star 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 uv is assigned the label θ(uv) = u³ + v³ + 3u²v + 3uv², then the resulting edge labels are distinct cube numbers. In this paper, we has investigated some families of graphs such as Path and Star.