On Legendre Product Cordial Labeling of Some Special Graphs

Jemina Clarisse C. Prudencio and Ricky F. Rulete
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Jemina Clarisse C. Prudencio: University of Southeastern Philippines, Philippines
Ricky F. Rulete: University of Southeastern Philippines, Philippines

European Journal of Mathematics and Statistics, 2025, vol. 6, issue 6, 1-12

Abstract: Let G be a connected graph of order n and let p be an odd prime. The bijective function f : V(G) → {1, 2, ..., n} is called a Legendre product cordial labeling modulo p, if there is an induced function f ∗ p : E(G) → {0, 1}, defined by f ∗ p(uv) = 0 whenever ([f (u)f (v)] /p) = −1 or f (u)f (v) ≡ 0 (mod p), and f ∗ p(uv) = 1 whenever ([f (u)f (v)] /p) = 1, which satisfies the condition ef ∗ p (0) − ef ∗ p (1) ≤ 1, where ef ∗ p (0) and ef ∗ p (1) are the number of edges with labels 0 and 1, respectively. In this study, we explored the Legendre product cordial labeling modulo p of Pp−1, Cp−1, Kp−1, Sp+1, Bp,p−1, K(p−1)/2,(p−1)/2, Gp,p−1, Combp, and DC(p−1)/2,(p−1)/2.

Keywords: Graph; legendre product cordial labeling; prime (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:epw:ejmath:v:6:y:2025:i:6:id:14418

DOI: 10.24018/ejmath.2025.6.6.418

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