Journals Information
Mathematics and Statistics Vol. 13(2), pp. 97 - 104
DOI: 10.13189/ms.2025.130204
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Structural Properties and Characteristic Polynomials of Cubic Power Graph of Dihedral Group
Mamika Ujianita Romdhini 1, Pankaj Rana 2,*, Amit Sehgal 3, Pooja Bhatia 2
1 Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Mataram, Mataram 83125, Indonesia
2 Department of Physical Sciences (Mathematics), Faculty of Sciences, Baba Mastnath University, Asthal Bohar (Rohtak), Haryana-124021, India
3 Department of Mathematics, Pt. NRS Government College, Rohtak, Haryana-124001, India
ABSTRACT
Cubic power graph of dihedral group 
having order 
and identity element 
, 
is a finite, simple, undirected graph for which two different vertices 
are adjacent if and only if 
or 
for some 
with 
. In this research, conditions on 
under which is planar, are calculated. Also conditions on under which is Hamiltonian, are calculated. It is also shown that is not an Eulerian graph. A polynomial that counts how many different ways there are to color a graph with a specific number of colors is called a chromatic polynomial. We have calculated the chromatic polynomial of when 
. Also chromatic polynomial of almost complete graph obtained by deleting 
number of non-adjacent edges is obtained. Spectral graph theory is a branch of mathematics that examines a graph's characteristics in relation to its characteristic polynomial, eigenvalues, and eigenvectors of related matrices, such as its adjacency matrix, Laplacian matrix or degree based matrices. Characteristic polynomials of degree based matrices such as Laplacian matrix, Signless Laplacian matrix, Maximum matrix, Minimum matrix and Greatest common divisor degree matrix of when .
KEYWORDS
Cubic Power Graph, Dihedral Group, Planar, Hamiltonian, Eulerian, Chromatic Polynomial, Degree of A Vertex Based Matrices
Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Mamika Ujianita Romdhini , Pankaj Rana , Amit Sehgal , Pooja Bhatia , "Structural Properties and Characteristic Polynomials of Cubic Power Graph of Dihedral Group," Mathematics and Statistics, Vol. 13, No. 2, pp. 97 - 104, 2025. DOI: 10.13189/ms.2025.130204.
(b). APA Format:
Mamika Ujianita Romdhini , Pankaj Rana , Amit Sehgal , Pooja Bhatia (2025). Structural Properties and Characteristic Polynomials of Cubic Power Graph of Dihedral Group. Mathematics and Statistics, 13(2), 97 - 104. DOI: 10.13189/ms.2025.130204.