Adjacency Matrix and Energy of Graph of a Ring Associated to Kapal Layar Pattern in Tudung Saji

Abstract

Tudung saji is a traditional food cover which is commonly used in Malaysia. In previous research, some triaxial patterns of tudung saji have been shown to be isomorphic to some groups. One of the common tudung saji pattern is called Kapal Layar (Sailboat), and this pattern is isomorphic to cyclic group of order six. Then, a new graph called tudung saji graph is introduced depending on the sections of the triaxial template of the tudung saji pattern. This graph is constructed with the set of vertices consisting of the elements of the Kapal Layar pattern in which two vertices are connected by an edge if the corresponding strands for both vertices are equal. Next, from the structure of the tudung saji graph of Kapal Layar pattern and the isomorphism of the pattern to the ring of integers modulo six, the adjacency matrix of the graph is constructed. Finally, the energy of graphs of the ring associated to Kapal Layar pattern is computed.