A Note on the Laplacian Energy of the Power Graph of a Finite Cyclic Group

Nurşah Mutlu Varlıoğlu; Şerife Büyükköse

Makale detayları

A Note on the Laplacian Energy of the Power Graph of a Finite Cyclic Group

Yazarlar:

Nurşah Mutlu Varlıoğlu | Şerife Büyükköse

Yayıncı:

Sakarya University

Ana Başlıklar:

Algebra and Number Theory | Pure Mathematics (Other)

Dergi:

Sakarya University Journal of Science Vol.28 Issue 2, pp.431-437

Belge Tipi:

Makale

Yayın Tarihi:

4/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001315409

pISSN:

2147-835X

Anahtar kelimeler:

Özet:

 In this study, the Laplacian matrix concept for the power graph of a finite cyclic group is redefined by considering the block matrix structure. Then, with the help of the eigenvalues of the Laplacian matrix in question, the concept of Laplacian energy for the power graphs of finite cyclic groups was defined and introduced into the literature. In addition, boundary studies were carried out for the Laplacian energy in question using the concepts the trace of a matrix, the Cauchy-Schwarz inequality, the relationship between the arithmetic mean and geometric mean, and determinant. Later, various results were obtained for the Laplacian energy in question for cases where the order of a cyclic group is the positive integer power of a prime.

 In this study, the Laplacian matrix concept for the power graph of a finite cyclic group is redefined by considering the block matrix structure. Then, with the help of the eigenvalues of the Laplacian matrix in question, the concept of Laplacian energy for the power graphs of finite cyclic groups was defined and introduced into the literature. In addition, boundary studies were carried out for the Laplacian energy in question using the concepts the trace of a matrix, the Cauchy-Schwarz inequality, the relationship between the arithmetic mean and geometric mean, and determinant. Later, various results were obtained for the Laplacian energy in question for cases where the order of a cyclic group is the positive integer power of a prime.

 In this study, the Laplacian matrix concept for the power graph of a finite cyclic group is redefined by considering the block matrix structure. Then, with the help of the eigenvalues of the Laplacian matrix in question, the concept of Laplacian energy for the power graphs of finite cyclic groups was defined and introduced into the literature. In addition, boundary studies were carried out for the Laplacian energy in question using the concepts the trace of a matrix, the Cauchy-Schwarz inequality, the relationship between the arithmetic mean and geometric mean, and determinant. Later, various results were obtained for the Laplacian energy in question for cases where the order of a cyclic group is the positive integer power of a prime.

 In this study, the Laplacian matrix concept for the power graph of a finite cyclic group is redefined by considering the block matrix structure. Then, with the help of the eigenvalues of the Laplacian matrix in question, the concept of Laplacian energy for the power graphs of finite cyclic groups was defined and introduced into the literature. In addition, boundary studies were carried out for the Laplacian energy in question using the concepts the trace of a matrix, the Cauchy-Schwarz inequality, the relationship between the arithmetic mean and geometric mean, and determinant. Later, various results were obtained for the Laplacian energy in question for cases where the order of a cyclic group is the positive integer power of a prime.

Makale detayları

A Note on the Laplacian Energy of the Power Graph of a Finite Cyclic Group

Yazarlar:

Nurşah Mutlu Varlıoğlu | Şerife Büyükköse

Yayıncı:

Sakarya University

Ana Başlıklar:

Algebra and Number Theory | Pure Mathematics (Other)

Dergi:

Sakarya University Journal of Science Vol.28 Issue 2, pp.431-437

Belge Tipi:

Makale

Yayın Tarihi:

4/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001315409

pISSN:

2147-835X

Cyclic Group

Laplacian Matrix

Laplacian Energy

Bound

Sayı

Makale detayları

A Note on the Laplacian Energy of the Power Graph of a Finite Cyclic Group

Yazarlar: Nurşah Mutlu Varlıoğlu | Şerife Büyükköse

Yayıncı: Sakarya University

Ana Başlıklar: Algebra and Number Theory | Pure Mathematics (Other)

Dergi: Sakarya University Journal of Science Vol.28 Issue 2, pp.431-437

Belge Tipi: Makale

Yayın Tarihi: 4/2024

Belge Dili: İngilizce

Document ID (Org No.): 2001315409

pISSN: 2147-835X

Cyclic Group

Laplacian Matrix

Laplacian Energy

Bound

Sayı

Yazarlar:

Nurşah Mutlu Varlıoğlu | Şerife Büyükköse

Yayıncı:

Sakarya University

Ana Başlıklar:

Algebra and Number Theory | Pure Mathematics (Other)

Dergi:

Sakarya University Journal of Science Vol.28 Issue 2, pp.431-437

Belge Tipi:

Makale

Yayın Tarihi:

4/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001315409

pISSN:

2147-835X