2013/12/30 by N. K. Sudev, Sudev, N. K., K. A. Germina +1 · 7 citations
Mathematics · #05C78 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05C78
paper · pdf · doi:10.48550/arxiv.1312.7674
12 pages. arXiv admin note: text overlap with arXiv:1312.7672
arxiv created 2014/03/24 · 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 f+:E(G) → 2ℕ0 defined by f+ (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 |f+(uv)|=max(|f(u)|,|f(v)|) and an IASI f is said to be a strong IASI if |f+(uv)|=|f(u)| |f(v)| for all u,v∈ V(G). In this paper, we discuss about a special type of integer additive set-indexers called arithmetic integer additive set-indexer and establish some results on this type of integer additive set-indexers. We also check the admissibility of arithmetic integer additive set-indexer by certain graphs associated with a given graph.