Journal of Applied and Pure Mathematics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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VECTOR BASIS S-CORDIAL LABELING OF BALLOON OF TRIANGULAR SNAKE GRAPH

  • R. PONRAJ (Department of mathematics, Sri Paramakalyani College) ;
  • R. JEYA (Department of Mathematics, Sri Paramakalyani College (Affiliated to Manonmaniam Sundaranar University))
  • Received : 2025.11.04
  • Accepted : 2026.03.03
  • Published : 2026.03.30
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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 each edge uv assign the label < 𝜑(u), 𝜑(v) >. We say that 𝜑 is a vector basis S-cordial labeling if |𝜑x - 𝜑y| ≤ 1 and |𝛾i - 𝛾j| ≤ 1 where 𝜑xdenotes the number of vertices labeled with the vector x and 𝛾i denotes the number of edges labeled with the scalar i. A graph with a vector basis S-cordial labeling is called a vector basis S-cordial graph. In this paper, we prove that the balloon of triangular snake graph is a vector basis S-cordial where S = { (1,1,1,1),(1,1,1,0),(1,1,0,0),(1,0,0,0) } is a basis in R4.

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Acknowledgement

The authors are highly thankful to the Reviewer for suggestions for revision which contributed to the improvement of the presentation of the paper.

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