Certain Types of Arithmetic Integer Additive set-indexers of Graphs
Sudev Naduvath, K. A. Germina · arXiv (Cornell University) · 2014
An integer additive set-indexer (IASI) is defined as an injective function f: V (G) → P(N0) such that the induced function f+: E(G) → P(N0) defined by gf (uv) = f(u)+f(v) is also injective, where N0 is the set of all non-negative integers. 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). 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. AMS Subject Classification: 05C78 1