Graceful labeling of zero-divisor graph Γ(ℤp²q) and Γ(ℤp³q)

Constantine, Christian (Bandung Institute of Technology)
Suwastika, Erma (Bandung Institute of Technology)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 13, No 2 (2025): Electronic Journal of Graph Theory and Applications

Some papers have already provided graceful labeling for some types of zero-divisor graphs. We reviewed the graceful labeling results of Γ(ℤ25), Γ(ℤ8), and Γ(ℤ27), then use those results to label zero-divisors graphs Γ(ℤ25q), Γ(ℤ8q), and Γ(ℤ27q).The result is that there is graceful labeling for Γ(ℤp²q) for p = 5 and Γ(ℤp³q) for p = 2, 3, where q is prime number that is different from p. In this paper, we provide the graceful labeling of zero-divisor graph Γ(ℤp²q) and Γ(ℤp³q) with adaptation and modification of existing results.