TY - JOUR
T1 - A Note on the Laplacian Energy of the Power Graph of a Finite Cyclic Group
AU - Mutlu Varlıoğlu, Nurşah
AU - Büyükköse, Şerife
PY - 2024
DA - April
Y2 - 2024
DO - 10.16984/saufenbilder.1369766
JF - Sakarya University Journal of Science
JO - SAUJS
PB - Sakarya University
WT - DergiPark
SN - 2147-835X
SP - 431
EP - 437
VL - 28
IS - 2
LA - en
AB - 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.
KW - Cyclic Group
KW - Laplacian Matrix
KW - Laplacian Energy
KW - Bound
CR - [1] A. V. Kelarev, S. J. Quinn, “A Combinatorial Property and Power Graphs of Groups,” Contribibutions to General Algebra, vol. 12, pp. 229-235, 2000.
CR - [2] A. V. Kelarev, S. J. Quinn, “Directed Graphs and Combinatorial Properties of Semigroups,” Journal of Algebra, vol. 251, no. 1, pp. 16-26, 2002.
CR - [3] A. V. Kelarev, S. J. Quinn, “A Combinatorial Property and Power Graphs of Semigroups,” Commentationes Mathematicae Universitatis Carolinae, vol. 45, no. 1, pp. 1-7, 2004.
CR - [4] I. Chakrabarty, S. Ghosh, M. K. Sen, “Undirected Power Graphs of Semigroups,” Semigroup Forum, vol. 78, pp. 410-426, 2009.
CR - [5] P. J. Cameron, “The Power Graph of AFinite Group II.,” Journal of Group Theory, vol. 13, no. 6, pp. 779-783, 2010.
CR - [6] P. J. Cameron, S. Ghosh, “The Power Graph of A Finite Group,” Discrete Mathematics, vol. 311, no. 13, pp. 1220-1222, 2011.
CR - [7] S. Chattopadhyay, P. Panigrahi, F. Atik, “Spectral Radius of Power Graphs on Certain Finite Groups,” Indagationes Mathematicae, vol.29, no. 2, pp. 730-737, 2018.
CR - [8] I. Gutman, “The Energy of Graph,” Berichteder Mathematisch Statistischen Sektion im Forschungszentrum Graz, vol. 103, pp. 1-22, 1978.
CR - [9] I. Gutman, B. Zhou, “Laplacian Energy of AGraph,” Linear Algebra and its Applications, vol. 414, no. 1, pp. 29-37, 2006.
UR - https://doi.org/10.16984/saufenbilder.1369766
L1 - https://dergipark.org.tr/en/download/article-file/3447972
ER -