Page 23 - POSTER FYP MAC-OGOS 2025

MAXIMUM DEGREE ENERGY OF K242/23
MAXIMUM DEGREE ENERGY OF

RELATIVE CO-PRIME GRAPHS FOR
RELATIVE CO-PRIME GRAPHS FOR

DIHEDRAL GROUPS D TO D 6
DIHEDRAL GROUPS D TO D

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nur elieni binti mukhtar

supervisor: dr norarida binti abd rhani

abstract
abstract

This research focuses on determining the maximum degree energy of the relative co-prime graphs of dihedral groups for D3 to D6. It involves

constructing the maximum degree matrices from graphs based on Sahrom (2025) and Mohd Subri (2025), calculating the characteristic

polynomials, and deriving eigenvalues to compute maximum degree energy. The results indicate that the maximum degree energy of the

relative co-prime graphs for D remains consistent due to the uniformity of the subgroup structure. However, for D , D , and D , the energy
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values vary, depending on the size of the original group and the orders of their subgroups. In addition, the subgroups associated with larger

groups and higher orders tend to yield higher maximum degree energies of the graph, meanwhile, the subgroups with smaller sizes and orders

result in lower energies. Based on these findings, it is recommended that future research explore the minimum degree energy of such graphs.

problem statement objectives
problem statement
objectives

RESEARCHERS’ STUDIES GAP IN RESEARCH 1. To determine the maximum degree matrix of the relative co-

prime graph of dihedral groups D from D to D .

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This study represents the There is still limited research 2. To determine the characteristic polynomial of the maximum

relationship between graph focused specifically on maximum degree matrix of the relative co-prime graph of dihedral groups

theory and group theory in degree energy of the relative D from D to D .

spectral graph theory. co-prime graphs for dihedral n 3 6

groups D to D . 3. To compute the maximum degree energy of the relative co-prime

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graph of dihedral groups D from D to D .
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methodology implementation
methodology
implementation

Start PHASE 1

Determine the maximum degree

matrix of the relative co-prime

graph for dihedral groups D to D .
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PHASE 1

Determine the maximum degree matrix

of the relative co-prime graph for

dihedral groups D to D . The relative co-prime graphs of
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D , D , D , and D are obtained

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from previous research by

PHASE 2 Sahrom (2025) and Mohd Subri

(2025). The graphs constructed

Determine the characteristic polynomial of based on Definition 3.2.4 and

the maximum degree matrix of the relative Definition 3.2.6.

co-prime graph for dihedral groups D to D .

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PHASE 2

Determine the characteristic

PHASE 3 PHASE 3 polynomial of the maximum degree

Compute the maximum degree energy of Compute the maximum degree matrix of the relative co-prime graph

the relative co-prime graph for energy of the relative co-prime for dihedral groups D to D .
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dihedral groups D to D . graph for dihedral groups D to D .
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End

results & Discussion
results & Discussion

conclusion recommendations
recommendations
conclusion

The objective of this project has been Conduct a research about the

achieved by applying all phase in minimum degree energy of the

methodology. The result shows the relative co-prime graphs of

maximum degree energy value that dihedral groups D to D .

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The maximum degree energy values increase on wanted to find by looking for maximum Condust an extended study on

the basis of increase in orders of the subgroups. degree matrices, characteristic maximum degree energy of

Subgroups associated with larger groups and polynomials and eigenvalues. It enhance relative co-prime graph for other

higher orders tend to yield higher maximum the understanding in spectral graph finite groups.

degree energies of the graph, meanwhile, the theory by analyzing the maximum

subgroups with smaller sizes and orders result in degree energy of the relative co-prime Extend o investigate the

lower energies. graphs of dihedral groups D to D . topological indices.
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