A Characterisation of Strong Integer Additive Set-Indexers of Graphs - Sudev, N. K.; Germina, K. A. (Communications in Mathematics and Applications, 2014)
Let N_0 be the set of all non-negative integers and P(N_0) be its power set. An integer additive set-indexer (IASI) is defined as an injective function f:V(G)→ P(N_0) such that the induced function f^+:E(G) → P(N_0) defined by f^+ (uv) = f(u)+ f(v) is also injective, where f(u)+f(v) is the sum set of f(u) and f(v). If f^+(uv)=k uvE(G), then f is said to be a k-uniform IASI. An IASI f is said to be a strong IASI if |f^+(uv)|=|f(u)|.|f(v)| uvE(G). In this paper, we study the characteristics of certain graph classes, graph operations and graph products that admit strong integer additive set-indexers.