On the hypergraphs associated with integer additive set-labeled graphs

International audienceLet N 0 denote the set of all non-negative integers and P(N 0) be its power set. An integer additive set-labeling (IASL) of a graph G is an injective set-valued function f : V (G) → P(N 0) such that the induced function f + : E(G) → P(N 0) is defined by f + (uv) = f (u) + f (v), where f (u) + f (v) is the sumset of f (u) and f (v). An IASL f of a graph G is said to be an integer additive set-indexer (IASI) of G if the associated function f + is also injective. A graph which admits an integer additive set-labeling (or integer additive set-indexer) is called an integer additive set-labeled graph (or integer additive set-indexed graph). In this paper, we initiate a study on the hypergraphs associated with the set-labels of integer additive set-labeled graphs