A study on the nourishing number of graphs and graph powers

Abstract

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)j = jf(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.