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A GRAPHICAL AND ZERO-ONE MATRICES
REPRESENTATIVE ON TAMPUK MANGGIS PATTERN
SATIRAH NISRINA BINTI NAWAWI | 2022467844 | K242/14
SUPERVISOR: MADAM MASNIRA BINTI RAMLI
ABSTRACT This study aims to explore the relationship between the mathematical concept and Malay culture, which is called ethnomathematics. It can be seen
in carvings, weaving, textile and painting. One of the Malay cultures is songket. Songket is a member of the brocade textile family, which includes
fabrics from Brunei, Indonesia, and Malaysia. The previous study focuses on the culture view, examining the patterns with some mathematical idea
such as geometrical concept. Therefore, this study explores one of the songket motif, Tampuk Manggis as the main subject discussed in a
mathematical framework. The vertices and edges are being identified in order to determine the graph of Tampuk Manggis pattern using GeoGebra
and Graph Online. The graph is analyzed based on properties such as planarity, degree, chromatic number, and connectivity, and represented as
zero-one matrix which are adjacency and incidence matrices. The study successfully presents five graph sketches that reflect the underlying
geometric connectivity of the pattern. This study emphasizes the potential of ethnomathematics in education and cultural preservation by
highlighting the analysis of the songket pattern in mathematical view. The findings promote more mathematical modeling of traditional patterns
and offer graph theory as a way for connecting cultural identification to current analytical tools.
PROBLEM STATEMENT OBJECTIVE
The Tampuk Manggis pattern is This study examined the study 1.To determine the graphs of the Tampuk Manggis pattern using
widely admired for its cultural Previous studies focused between the patterns GeoGebra and Graph Online.
and aesthetic value, but its on symmetry or geometric specifically Tampuk Manggis 2.To find the graph properties of the Tampuk Manggis pattern.
mathematical structure has aspects. with graph theory through zero- 3.To represent the Tampuk Manggis pattern as a zero-one matrix.
been largely unexplored. one matrix
METHODOLOGY & IMPLIMENTATION 1. TYPE OF GRAPH: 5. DEGREE OF VERTEX:
UNDIRECTED, SIMPLE, • CENTER VERTEX HAS DEGREE 4
CONNECTED, PLANAR, • OUTER VERTICES EACH HAVE DEGREE 1
TREE AND STAR 6. REGION: 1
2. VERTEX: 5 7. VERTEX-CONNECTIVITY: 1
3. EDGES: 4
4. LOOP: 0 8. CHROMATIC NUMBER: 2
IDENTIFY GRAPH PROPERTIES
START IDENTIFY THE VERTICES AND EDGES TRANSFORM THE PATTERN TO A GRAPH CLASSIFICATION END
DEFINE ZERO-ONE MATRICES
Adjacency matrix Incidence matrix
RESULT & DISCUSSION
GRAPH 1 GRAPH 2 GRAPH 3 GRAPH 4 GRAPH 5
UNDIRECTED, SIMPLE, CONNECTED, UNDIRECTED, SIMPLE, CONNECTED, UNDIRECTED, SIMPLE, CONNECTED, UNDIRECTED, SIMPLE, CONNECTED, UNDIRECTED, CONNECTED, PLANAR AND
TYPE OF GRAPH PLANAR, TREE AND STAR PLANAR, TREE AND STAR PLANAR AND STAR PLANAR AND STAR MULTIGRAPH
NO. OF VERTICES 5 9 25 33 9
NO. OF EDGES 4 8 32 40 16
NO. OF LOOP 0 0 0 0 8
REGION 1 1 9 9 9
VERTEX-CONNECTICTY 1 1 1 1 1
CHROMATIC NO. 2 2 3 3 2
CENTER VERTEX HAS DEGREE 4 CENTER VERTEX HAS DEGREE 8 CENTER VERTEX HAS 8 DEGREE. CENTER VERTEX HAS 8 DEGREE. CENTER VERTEX HAS 4 DEGREE
DEGREE OF VERTEX CORNER VERTICES (OUTERMOST) HAVE
OUTER VERTICES EACH HAVE DEGREE 1 OUTER VERTICES EACH HAVE DEGREE 1 CORNER VERTICES (OUTERMOST) HAVE DEGREE 2. OUTER VERTICES EACH HAVE DEGREE 2
DEGREE 2. SIDE VERTICES (ON THE EDGES BUT NOT
SIDE VERTICES (ON THE EDGES BUT NOT CORNERS) HAVE DEGREE 2.
CORNERS) HAVE DEGREE 2. ANOTHER SIDE VERTICES ( THE MOST FAR WITH
OTHER MIDDLE VERTICES (EXCLUDING THE OTHER MIDDLE VERTICES) HAVE DEGREE 2.
CENTER)HAVE DEGREE 3. OTHER MIDDLE VERTICES (EXCLUDING CENTER)
HAVE DEGREE 3.
ADJACENCY MATRIX
INCIDENCE MATRIX
CONCLUSION RECOMMENDATION
Varieties of graphs can be Graph and zero-one matrices can Utilizing computer tools to Discussed in more detail to the Undirected graph of this motif
designed according to the be defined in order to represent automate matrix creation and aspect of spectrum of the graph also can be purpose as the
vertices and edges. the Tampuk Manggis pattern. graph extraction. or the energy of the graph. subject of the next research
