# Topological Integer Additive Set-Graceful Graphs

Source: [Topological Integer Additive Set-Graceful Graphs](<https://www.sota2.com/research/paper/68fa52511e209131ce97a2ed>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-28T13:55:37.128Z

Authors: N. K. Sudev, K. A. Germina, K. P. Chithra

Published: 2015-06-03T13:17:30.000Z

## 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 $f(V(G))\\cup \\{\\emptyset\\}$ 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 $f^+$, $f^+(E(G))= \\mathcal{P}(X)-\\{\\emptyset, \\{0\\}\\}$. 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 $G$.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1506.01240>)

[PDF](<https://arxiv.org/pdf/1506.01240.pdf>)