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with diameter . The chromatic number and clique
number of these graphs are found and a bound for
the independence number is obtained. The
conjugacy class graphs of are found to be
both Eulerian and Hamiltonian for certain values of
and .
To summarize, the conjugacy class graphs
related to the direct product of dihedral groups are
constructed using the size of conjugacy classes of
dihedral groups, which allowed us to obtain
different parameters of the concerned graphs.
The method followed herein to obtain these
results can be extended to any non-abelian group
for which the conjugacy classes can be found,
manually or with the help of a computer.
Work is in progress to compute the conjugacy
classes related to the direct product of symmetric
and alternating groups and thereby obtain the graph
structures for these groups.
5 Future Study
The generalized conjugacy class graphs of dihedral
groups and generalized quaternion groups and their
related direct product graphs can be found. Also,
the partition dimension of conjugacy class graphs
related to the above-mentioned groups will be an
interesting topic of further research, and bounds for
partition dimension can be established, if it exists.
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Contribution of Individual Authors to the
Creation of a Scientific Article (Ghostwriting
Policy)
On behalf of all the authors, the corresponding
author states that the manuscript is an original work
of the authors and all authors made a significant
contribution to this paper.
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
The authors declare that there is no conflict of
interest.
Conflict of Interest
No funding was received for conducting this study.
This manuscript has not been submitted for
publication elsewhere and has not been published
in any other journal.
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WSEAS TRANSACTIONS on MATHEMATICS
DOI: 10.37394/23206.2024.23.48
Chinmayee Kumar, Kuntala Patra