On Integer Additive Set-Sequential Graphs

International audienceA set-labelling of a graph G is an injective function f : V (G) → P(X), where X is a finite set of non-negative integers and a set-indexer of G is a set-labeling such that the induced function f ⊕ : E(G) → P(X) − {∅} defined by f ⊕ (uv) = f (u)⊕f (v) for every uv∈E(G) is also injective. A set-indexer f : V (G) → P(X) is called a set-sequential labeling of G if f ⊕ (V (G) ∪ E(G)) = P(X) − {∅}. A graph G which admits set-sequential labelling is called a set-sequential graph. An integer additive set-labeling is an injective function f : V (G) → P(N 0 ), N 0 is the set of all non-negative integers and an integer additive set-indexer is an integer additive set-labeling such that the induced function f + : E(G) → P(N 0 ) defined by f + (uv) = f (u) + f (v) is also injective. In this paper, we extend the concepts of set-sequential labelling to integer additive set-labellings of graphs and provide some resultson them