Vector basis {(1,1,1,1),(1,1,1,0),(1,1,0,0),(1,0,0,0)}-cordial labeling of certain trees and flower 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 φx denotes the number of vertices labeled with the vector x and γi 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 {(1,1,1,1),(1,1,1,0),(1,1,0,0),(1,0,0,0)}-cordial labeling behavior of some new graphs like the olive tree, lobster graph, Im,n graph, shrub graph, rose flower graph, clematis flower graph, cherry blossom flower graph, armed crown graph, rocket graph and sandat graph.