Nourishing Number of Some Associated Graphs

Let N0 = N∪{0} and P(N0) be the power set. An injection f : V (G) → P(N0) is an integer additive set-indexer (IASI) of a graph G if the induced map f+ : E(G) → P(N0) given by f+(uv) = f(u) + f(v) is also an injection, where f(u) + f(v) is the sumset of f(u) and f(v). Moreover, if |f+(uv)| = |f(u)| |f(v)|, for all uv in E(G), then f is a strong IASI of G. The nourishing number of a graph G is the minimum order of the maximal complete subgraph of G such that G admits a strong IASI. In this paper we investigate the admissibility of strong IASI for some associated graphs and calculate their nourishing number. In addition, we obtain the nourishing number of powers of the associated graphs.