Vector basis S-cordial labeling of graphs with applications in biological models

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 \(\phi: V(G) \rightarrow S\) be a function. For edge \(uv\) assign the label \(<\phi(u),\phi(v)>\). Then \(\phi\) is called a vector basis \(S\)-cordial labeling of \(G\) if \(|\phi_{x}-\phi_{y}|\leq 1\) and \(|\gamma_i-\gamma_j |\leq 1\) where \(\phi_{x}\) denotes the number of vertices labeled with the vector \(x\) and \(\gamma_i\) 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 examine the vector basis {(1,1,1,1),(1,1,1,0),(1,1,0,0),(1,0,0,0)}-cordial labeling behaviour of Mongolian tent and parachute graph such a labeling finds applications in biological modelling.