Document Type : Research Paper

Authors

• R Ponraj ¹
• R Jeya ²

¹ Department of Mathematics Sri Parakalyani College Alwarkurichi -627 412, India

² Department of Mathematics, Sri Paramakalyani College, Alwarkurichi-627412, Tamilnadu, India

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 $\omega_{1}$ and $\omega_{2}$ by $<\omega_{1},\omega_{2}>$. Let $\chi: V(G) \rightarrow S$ be a function. For edge $uv$ assign the label $<\chi(u),\chi(v)>$. Then $\chi$ is called a vector basis $S$-cordial labeling of $G$ if $|\chi_{\omega_{1}}-\chi_{\omega_{2}}|\leq 1$ and $|\delta_i-\delta_j |\leq 1$ where $\chi_{\omega_{i}}$ denotes the number of vertices labeled with the vector $\omega_{i}$ and $\delta_i$ 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 prove that the graphs $L_{n}\odot mK_{1}$ and $T(P_{n})\odot mK_{1}$ are the vector basis $\{(1,1,1,1), (1,1,1,0), (1,1,0,0), (1,0,0,0)\}$-cordial.

Keywords

• path
• ladder
• complete graph
• cycle
• total graph