A Study on the Nourishing Number of Graphs and Graph Powers

Let N0 be the set of all non-negative integers and P(N0) be its power set. Then, an integer additive set-indexer (IASI) of a given graph G is defined as an injective function f : V (G) → P(N0) such that the induced edge-function f : E(G) → P(N0) defined by f(uv) = f(u) + f(v) is also injective, where f(u) + f(v) is the sumset of f(u) and f(v). An IASI f of G is said to be a strong IASI of G if |f(uv)| = |f(u)| |f(v)| for all uv ∈ E(G). The nourishing number of a graph G is the minimum order of the maximal complete subgraph of G so that G admits a strong IASI. In this paper, we study the characteristics of certain graph classes and graph powers that admit strong integer additive set-indexers and determine their corresponding nourishing numbers.