Journals Information
Mathematics and Statistics Vol. 13(3), pp. 127 - 135
DOI: 10.13189/ms.2025.130301
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Degree Based Matrices of Co-prime Order Graph of Finite Groups
Manjeet Saini 1,*, Vijeta Kumari 1, Pankaj Rana 2, Amit Sehgal 3, Dalip Singh 1
1 Department of Mathematics, Maharshi Dayanand University, Rohtak 124001, India
2 Department of Physical Sciences (Mathematics), Baba Mastnath University, Asthal Bohar, Rohtak 124021, India
3 Department of Mathematics, Pt. Neki Ram Sharma Govt. College, Rohtak 124001, India
ABSTRACT
The co-prime order graph of a group is a simple finite graph having vertex set as group itself, and there is an edge between vertex 
to the other vertex 
whenever 
or prime. Spectral graph theory is the study of the properties of a graph in relationship to the characteristic polynomial, eigenvalues, and eigenvectors of matrices associated with the graph, such as its adjacency matrix, Laplacian matrix, signless Laplacian matrix, normalized Laplacian matrix, maximum degree matrix, minimum degree matrix, etc. In this article, we have extended the study from the Laplacian matrix spectrum to various degree based matrices such as signless Laplacian matrix, normalized Laplacian matrix, maximum degree and minimum degree matrix of co-prime order graph of finite groups 
, 
and also provided some general results for any finite group. Laplacian matrix, signless Laplacian matrix and normalized Laplacian matrix are based on adjacency matrix and degree matrix. The maximum degree matrix is based on the maximum of degree of a vertex among all the pairs of vertices whereas the minimum degree matrix is based on the minimum of degree of a vertex among all the pairs of vertices.
KEYWORDS
Co-prime Order Graph, Finite Group, Laplacian Matrix, Signless Laplacian Matrix, Maximum Matrix, Minimum Matrix
Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Manjeet Saini , Vijeta Kumari , Pankaj Rana , Amit Sehgal , Dalip Singh , "Degree Based Matrices of Co-prime Order Graph of Finite Groups," Mathematics and Statistics, Vol. 13, No. 3, pp. 127 - 135, 2025. DOI: 10.13189/ms.2025.130301.
(b). APA Format:
Manjeet Saini , Vijeta Kumari , Pankaj Rana , Amit Sehgal , Dalip Singh (2025). Degree Based Matrices of Co-prime Order Graph of Finite Groups. Mathematics and Statistics, 13(3), 127 - 135. DOI: 10.13189/ms.2025.130301.