2013/12/31 by N. K. Sudev, K. A. Germina · 3 citations
Mathematics · #math.CO #msc:05C78
published as International J. of Math. Sci. & Engg. Appls. (IJMSEA), Vol. 8 No. II, 11-22, 2014 · 12 pages. arXiv admin note: text overlap with arXiv:1312.7674 To Appear in Int. J. Math. Sci.& Engg. Appl. in March 2014
arxiv created 2014/03/02 · arxiv updated 2014/03/25
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 \em weak IASI if |gf(uv)|=max(|f(u)|,|f(v)|) and an IASI f is said to be a \em 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.