Vector Basis S-Cordial Labeling of Graphs

Abstract

Let G be a (p, q) graph. Let V be an inner product space with basis S. We denote the inner product of the vectors x and y by <x, y>. Let φ: V(G)→S be a function. For edge uv assign the label <ϕ(u), ϕ(v)>. Then ϕ is called a vector basis S-cordial labeling of G if |φ_x−φ_y|≤1 and |γ_i-γ_j|≤1 where φ_x denotes the number of vertices labeled with the vector x and γ_i denotes the number of edges labeled with the scalar i. A graph which admits a vector basis S-cordial labeling is called a vector basis S-cordial graph. In this paper, we investigate the vector basis S-cordial labeling behavior of certain standard graphs like path, cycle, complete graph and star graph.