On Integer Additive set-Sequential Graphs

Abstract

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 $f^{\oplus }:E(G)\to \mathcal{P}(X)-\{\varnothing \}$ 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 $f^{\oplus }(V(G)\cup E(G))=\mathcal{P}(X)-\{\varnothing \}$. A graph $G$ which admits a set-sequential labeling is called a set-sequential graph. An integer additive set-labeling is an injective function $f:V(G)\to \mathcal{P}({\mathbb{N}}_0)$, ${\mathbb{N}}_0$ 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 $f^{+}:E(G)\to \mathcal{P}({\mathbb{N}}_0)$ 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.

11 pages, 2 figures, submitted. arXiv admin note: substantial text overlap with arXiv:1403.3984, arXiv:1407.4533

References in corpus (1)

• On Integer Additive Set-Indexers of Graphs

Cited by in corpus (2)

• On Integer Additive Set-Filtered Graphs
• Topological Integer Additive Set-Sequential Graphs