PRIME AND CO-PRIME EDGE ANTI-MAGIC VERTEX LABELING OF FAMILIES OF UNICYCLIC GRAPHS IN SENSOR NETWORK

Chitra G., Clement Joe Anand M., Ittanagi B. M., Ranjitha B., CANGÜL İ. N.

Turkish World Mathematical Society Journal of Applied and Engineering Mathematics, vol.15, no.1, pp.17-26, 2025 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 15 Issue: 1
  • Publication Date: 2025
  • Journal Name: Turkish World Mathematical Society Journal of Applied and Engineering Mathematics
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.17-26
  • Keywords: anti-magic labeling, co-prime labeling, hairy cycles, odd-prime labeling, Prime labeling, sensor network
  • Bursa Uludag University Affiliated: Yes

Abstract

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.