Associated graphs of certain arithmetic IASI graphs

Let $mathbb{N}_0$ be the set of all non-negative integers and $mathcal{P}(mathbb{N}_0)$ be its power set. An integer additive set-indexer (IASI) is defined as an injective function $f:V(G)to mathcal{P}(mathbb{N}_0)$ such that the induced function $f^+:E(G) to mathcal{P}(mathbb{N}_0)$ defined by $f^+ (uv) = f(u)+ f(v)$ is also injective, where $f(u)+ f(v)$ is the sum set of the sets $f(u)$ and $f(v)$. A graph $G$ which admits an IASI is called an IASI graph. An arithmetic integer additive set-indexer is an integer additive set-indexer $f$, under which the set-labels of all elements of a given graph $G$ are the sets whose elements are in arithmetic progressions. In this paper, we discuss the admissibility of arithmetic integer additive set-indexers by certain associated graphs of the given graph $G$, like line graph, total graph and the like.