Vertex Sum Cube Labeling for Some Special Graphs

Abstract

In this chapter, the new concept vertex sum cube labeling has been introduced and a formula for vertex sum cube labeling has been established. A function \(\theta\) 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 \(\mathit{uv}\) is assigned the label \(\theta\)(\(\mathit{uv}\)) = \(\mathit{u^3}\) + \(\mathit{v^3}\) + \(\mathit{3u^2v}\) + \(\mathit{3uv^2}\), then \(\theta\) is a bijective function, then the resulting edge labels are distinct cube numbers. In this chapter, some families of graphs such as Ladder, Stair Str\(_n\), Jelly Fish \(\mathit{J(m,n)}\) and P\(^2_n\) has been established.