On Integer Additive Set-Indexers of Graphs

Original · EN

A set-indexer of a graph G is an injective set-valued function f:V(G) →2ˣ such that the function f⊕:E(G)→2ˣ-{} defined by f⊕(uv) = f(u)⊕ f(v) for every uv∈ E(G) is also injective, where 2ˣ is the set of all subsets of X and ⊕ is the symmetric difference of sets. An integer additive set-indexer is defined as an injective function f:V(G)→ 2ⁿ⁰ such that the induced function gf:E(G) → 2ⁿ⁰ defined by gf (uv) = f(u)+ f(v) is also injective. A graph G which admits an IASI is called an IASI graph. An IASI f is said to be a weak IASI if |gf(uv)|=max(|f(u)|,|f(v)|) and an IASI f is said to be a strong IASI if |gf(uv)|=|f(u)| |f(v)| for all u,v∈ V(G). In this paper, we study about certain characteristics of inter additive set-indexers.