PRIME AND CO-PRIME EDGE ANTI-MAGIC VERTEX LABELING OF FAMILIES OF UNICYCLIC GRAPHS IN SENSOR NETWORK
Turkish World Mathematical Society Journal of Applied and Engineering Mathematics, cilt.15, sa.1, ss.17-26, 2025 (ESCI, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 15 Sayı: 1
- Basım Tarihi: 2025
- Dergi Adı: Turkish World Mathematical Society Journal of Applied and Engineering Mathematics
- Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
- Sayfa Sayıları: ss.17-26
- Anahtar Kelimeler: anti-magic labeling, co-prime labeling, hairy cycles, odd-prime labeling, Prime labeling, sensor network
- Bursa Uludağ Üniversitesi Adresli: Evet
Özet
A finite simple undirected graph containing p vertices and q edges is called as prime anti-magic if it has an injection from the vertex set of integers {1, 2, …, p} satisfying that for each edge uv, the labels given to u and v are relatively coprime and the induced edge labels generated by f(uv) = f(u) + f(v) are all distinct. If the vertices have been assigned a prime labeling, then the graph is called co-prime. In this article, we study some new classes of unicyclic graphs that admits prime and co-prime anti-magic labelings. Also, they are satisfied with the condition of odd prime anti-magic labeling. Thus, this prime and co-prime anti-magic labeling could serve as a surveillance or security model for various kinds of buildings.