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

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

G. Chitra, M. Clement Joe Anand, Basavaraj M. Ittanagi, B. Ranjitha, I. N. Cangul

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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.

Keywords

Prime labeling, co-prime labeling, odd-prime labeling, anti-magic labeling, hairy cycles, sensor network.