An integer additive set-indexer is defined as an injective function, then f is said to be a k-uniform integer additive set-indexers. An integer additive set-indexer f is said to be a strong integer additive setindexer if |g f (uv)| = |f (u)|.|f (v)| ∀ uv ∈ E(G). We already have some characteristics of the graphs which admit strong integer additive set-indexers. In this paper, we study the characteristics of certain graph classes, graph operations and graph products that admit strong integer additive set-indexers.
We have the notion of set-indexers, integer additive set-indexers and k-uniform integer additive set-indexers of graphs. In this paper, we initiate a study of the graphs which admit k-uniform integer additive set-indexers and introduce the notion of weakly uniform integer additive set-indexers and arbitrarily uniform integer additive setindexers and provide some useful results on these types of set-indexers.
Mathematics Subject Classification: 05C78
Let N0 be the set of all non-negative integers. An integer additive setindexer of a graph G is an injective function f :is also injective. An IASI is said to be k-uniform if |f + (e)| = k for all e ∈ E(G). In this paper, we introduce the notions of strong integer additive setindexers and initiate a study of the graphs which admit strong integer additive set-indexers.
Let N 0 denote the set of all non-negative integers and P(N 0 ) be its power set. An integer additive set-indexer (IASI) of a graph G is an injective function f :is also injective, where N 0 is the set of all non-negative integers. A graph G which admits an IASI is called an IASI graph. An IASI of a graph G is said to be an arithmetic IASI if the elements of the set-labels of all vertices and edges of G are in arithmetic progressions. In this paper, we discuss about two special types of arithmetic IASIs.Key words: Integer additive set-indexers, uniform integer additive set-indexers, arithmetic integer additive set-indexers, isoarithmetic integer additive set-indexers, biarithmetic integer additive set-indexer.
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