Topological Integer Additive Set-Graceful Graphs

Abstract

Let ${\mathbb{N}}_0$ denote the set of all non-negative integers and $X$ be any subset of $X$. Also denote the power set of $X$ by $\mathcal{P}(X)$. An integer additive set-labeling (IASL) of a graph $G$ is an injective function $f:V(G)\to \mathcal{P}(X)$ such that the induced function $f^{+}:E(G)\to \mathcal{P}(X)$ 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 $f$ is said to be a topological IASL (Top-IASL) if $f(V(G))\cup \{\varnothing \}$ is a topology of the ground set $X$. An IASL is said to be an integer additive set-graceful labeling (IASGL) if for the induced edge-function $f^{+}$, $f^{+}(E(G))=\mathcal{P}(X)-\{\varnothing ,\{0\}\}$. In this paper, we study certain types of IASL of a given graph $G$, which is a topological integer additive set-labeling as well as an integer additive set-graceful labeling of $G$.

9 pages, 2 figure, submitted

References in corpus (1)

• On Weakly Uniform Integer Additive Set-Indexers of Graphs

Cited by in corpus (1)

• Topological Integer Additive Set-Sequential Graphs