Construction of additively graceful signed graphs-I

TL;DR

This paper presents methods for constructing additively graceful signed graphs from various graphs and determines specific conditions under which certain graphs admit such labelings.

Contribution

It introduces new construction techniques for additively graceful signed graphs and identifies parameter conditions for non-divisible sum graphs to be additively graceful.

Findings

Constructed additively graceful signed graphs from arbitrary graphs.

Derived conditions for parameters m, n in G(m, n) to admit additively graceful labeling.

Extended existing methods to generate new classes of additively graceful signed graphs.

Abstract

In this paper, we construct additively graceful signed graphs S from a given graph G that may be additively graceful or not be additively graceful. We also show the construction of additively graceful signed graphs from additively graceful signed graphs. We find the values of m, n in non-divisible sum graph, denoted as G(m, n), that admit additively graceful labeling.