Graceful Antimagic Labelling of Disconnected Graphs

Phook, Jun Wen (2026) Graceful Antimagic Labelling of Disconnected Graphs. Final Year Project (Bachelor), Tunku Abdul Rahman University of Management and Technology.

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Abstract

This project investigates the existence of Graceful Antimagic Labelling (GAL) and 2-Component Graceful Antimagic Labelling (2CGAL) for several families of disconnected graphs. The study focuses on three main types of graph structures: the disjoint union of cycle and path graphs, Cn ∪ Pm, the disjoint union of two cycle graphs, Cn ∪ Cm and the disjoint union of two star graphs, Sp ∪ Sq. A general theorem was successfully established for Sp ∪ Sq for all integers p ≥ q ≥ 2, proving that this graph structure admits a valid 2CGAL. For other types of graph structures, several valid labelling configurations were obtained through computational search and pattern observation, which led to conjectures regarding the existence of GAL. Overall, this project provides new insights into GAL for disconnected graphs and suggests directions for further research in graph labelling theory.