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Ponraj, R, Jeya, R. (1404). 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. , 57(1), 30-40. doi: 10.22059/jac.2025.391907.1226
R Ponraj; R Jeya. "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". , 57, 1, 1404, 30-40. doi: 10.22059/jac.2025.391907.1226
Ponraj, R, Jeya, R. (1404). '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', , 57(1), pp. 30-40. doi: 10.22059/jac.2025.391907.1226
Ponraj, R, Jeya, R. 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. , 1404; 57(1): 30-40. doi: 10.22059/jac.2025.391907.1226

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

Journal of Algorithms and Computation
مقاله 3، دوره 57، شماره 1، آبان 2025، صفحه 30-40    اصل مقاله (732.86 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22059/jac.2025.391907.1226
نویسندگان
R Ponraj* 1؛ R Jeya2
1Department of Mathematics Sri Parakalyani College Alwarkurichi -627 412, India
2Department of Mathematics, Sri Paramakalyani College, Alwarkurichi-627412, Tamilnadu, India
چکیده
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.
کلیدواژه‌ها
path؛ ladder؛ complete graph؛ cycle؛ total graph
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