Exploring Graph Isomorphism of Pucuk Rebung Ornaments

Abstract

Pucuk Rebung ornaments are widely recognized in Malaysia, particularly in traditional textiles such as songket, batik sarong, and limar cloth. The Pucuk Rebung pattern has many variations across the Southest Asia, particularly in Malaysia, Indonesia and Thailand. In this study, Pucuk Rebung patterns from Malaysia are highlighted for four different pattern variations through graph isomorphism. A major challenge in studying traditional motifs is the lack of a systematic approach to quantify and compare their structural similarities. Traditional analyses rely heavily on visual interpretation, making it difficult to determine the uniqueness of each pattern mathematically. To address this issue, this study employs a graph-theoretical approach by transforming Pucuk Rebung patterns into zero-one matrices through image processing. Then, the corresponding graphs based on the zero-one matrices are created, and analyzing their structural similarities using graph isomorphism. The findings suggest that no Pucuk Rebung patterns are isomorphic, which confirms the originality of each Pucuk Rebung pattern. Through the study, it emphasises the efficacy of graph theory in mathematically distinguishing traditional motifs, thereby facilitating a more profound comprehension of their structural characteristics through the context of mathematical theory.