A set-labeling of a graph $G$ is an injective function $f:V(G)\to \mathcal{ P}(X)$, 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 $f^{ \oplus}:E(G)\rightarrow \mathcal{ P}(X)-\{ \emptyset\}$ defined by $f^{ \oplus}(uv) = f(u){ \oplus}f(v)$ for every $uv{ \in} E(G)$ is also injective. A set-indexer $f:V(G)\to \mathcal{ P}(X)$ is called a set-sequential labeling of $G$ if $f^{ \oplus}(V(G)\cup E(G))=\mathcal{ P}(X)-\{ \emptyset\}$. A graph $G$ which admits a set-sequential labeling is called a set-sequential graph. An integer additive set-labeling is an injective function $f:V(G)\rightarrow \mathcal{ P}(\mathbb{ N}_0)$, $\mathbb{ N}_0$ 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 $f^+:E(G) \rightarrow \mathcal{ P}(\mathbb{ N}_0)$ defined by $f^+ (uv) = f(u)+ f(v)$ is also injective. In this paper, we extend the concepts of set-sequential labeling to integer additive set-labelings of graphs and provide some results on them.
Categories: math.CO