Some Results on Additively Graceful Signed Stars and Double Stars

TL;DR

This paper investigates additively graceful labelings of signed stars and double stars, providing characterizations and existence results for various subclasses, highlighting the complexity differences between the two graph types.

Contribution

It offers a complete characterization for signed stars and new existence, uniqueness, and non-existence results for subclasses of signed double stars.

Findings

Characterization of additively graceful signed stars.

Existence and non-existence results for certain signed double star subclasses.

Complexity increase from signed stars to signed double stars.

Abstract

We study additively graceful labelings of signed graphs on stars and double stars. While the case of signed stars is straightforward, the problem becomes significantly more intricate for signed double stars. We obtain a characterization of additively graceful signed stars, while, for several sub-classes of additively graceful signed double stars, we establish existence, uniqueness and non-existence results.