Vector Basis {(1, 1, 1, 1), (1, 1, 1, 0), (1, 1, 0, 0), (1, 0, 0, 0)}-Cordial Labeling of Ln ⊙ mK1 and T(Pn) ⊙ mK1

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Ponraj R.; Jeya R.

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Journal Paper

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Journal: JOURNAL OF ALGORITHMS AND COMPUTATION Year:2025 | Volume:57 | Issue:1 Page(s): 30-40

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Title

Vector Basis {(1, 1, 1, 1), (1, 1, 1, 0), (1, 1, 0, 0), (1, 0, 0, 0)}-Cordial Labeling of Ln ⊙ mK1 and T(Pn) ⊙ mK1

Author(s)

Ponraj R. | Jeya R. | Issue Writer Certificate

Keywords

Path

ladder

complete graph

cycle

total graph

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.

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