Page 20 - POSTER FYP MAC-OGOS 2025

FIRST ZAGREB, SECOND ZAGREB AND WIENER INDICES FOR K242/20

n-TH COPRIME GRAPH OF DIHEDRAL GROUP OF ORDER EIGHT, D 4

NURUL ZAHIRA FITRIYAH BINTI ZAHARI (2022457952)

SUPERVISOR: DR FADILA NORMAHIA BINTI ABD MANAF

ABSTRACT METHOD & IMPLEMENTATION

This project explores the n-th coprime PHASE 1: Construct the n-th coprime graph of

graph of the Dihedral group of order Dihedral group of order eight, D 4

eight, D using topological indices: the
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first Zagreb index, second Zagreb index,

and Wiener index. The group elements

are represented in terms of generators a

and b, and graphs are constructed by

connecting vertices with GCD equal to n.

The structure of each graph is analyzed,

and topological indices are calculated to

observe how graph structure influences

their values. This research shows how

algebraic structures can be interpreted PHASE 3: Determine the second Zagreb index

using graph theory, with potential of n-th coprime graph of D

applications in chemistry and network PHASE 2: Determine the first Zagreb index 4

of n-th coprime graph of D

analysis 4

PROBLEM STATEMENT

Understanding the structure of algebraic

groups through graph theory can

PHASE 4: Determine the Wiener
provide deeper insights into both index of n-th coprime graph of D

mathematical theory and practical 4

applications, such as chemistry and

network analysis. However, there is

limited research on how topological

indices behave when applied to coprime

graphs of specific groups like the

Dihedral group, D . This study addresses

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the gap by investigating how different

values of n affect the structure of n-th

coprime graphs and how these changes RESULT & DISCUSSION

influence the first Zagreb index, second

Zagreb index, and Wiener index. The goal

is to understand the relationship

between group structure and graph-

based numerical properties

OBJECTIVES

1. To construct the n-th coprime

graph of Dihedral group of order

eight, D .
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2. To determine the first Zagreb index

of n-th coprime graph of D .

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CONCLUSION RECOMMENDATION

3. To determine the second Zagreb

index of n-th coprime graph of D . This project shows how the structure of n-th coprime graphs of

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the Dihedral group D affects the values of topological indices. For future studies, it is recommended to explore other
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4. To determine the Wiener index of When the graph is more connected (like in a complete tripartite algebraic groups, such as larger Dihedral groups or cyclic

graph), the indices are higher. When the graph has fewer
groups, to see how their coprime graphs behave. Researchers
n-th coprime graph of D . connections (like in a star graph), the indices are lower. These can also try using more topological indices to get deeper
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findings help us understand how group theory and graph insights. Additionally, applying these findings in real-world

theory can work together and suggest that this method can be fields like chemistry, cryptography, or network analysis could

used to study other algebraic groups in the future. make the research more practical and meaningful.