ON THE SPECTRUM AND CONNECTIVITY OF INVERSE GRAPH OF A GENERALIZED QUATERNION GROUP
We study the spectrum and connectivity of the inverse graph of a generalized quaternion group.
inverse graph, characteristic polynomial, adjacency matrix, Laplacian matrix, adjacency spectrum, Laplacian spectrum, algebraic connectivity
Received: June 13, 2024; Revised: July 29, 2024; Accepted: August 20, 2024; Published: September 2, 2024
How to cite this article: Makkiah Suleiman Makki, On the spectrum and connectivity of inverse graph of a generalized quaternion group, Advances and Applications in Discrete Mathematics 41(7) (2024), 565-580. https://doi.org/10.17654/0974165824037
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
References:
[1] M. R. Alfuraidan and Y. F. Zakariyai, Inverse graphs associated with finite groups, Elect. J. Graph Theory and Appl. 5(1) (2017), 142-154.[2] N. Biggs, Algebraic Graph Theory, 2nd ed., Cambridge University Press, New York, 1993.[3] A. E. Brouwer and W. H. Haemers, Spectra of graphs, Monograph, Springer, New York, 2011.[4] M. Fiedler, Algebraic connectivity of graphs, Czechoslovak Math. J. 23(2) (1973), 298-305.[5] M. Fiedler, Laplacian of graphs and algebraic connectivity, Banach Center Publ. 25(1) (1989), 57-70.[6] M. Ghorbani and M. Songhori, On the spectrum of Cayley graphs, Algebra Discrete Math. 30(2) (2020), 194-206.[7] A. Hofman, On eigenvalues and colorings of graphs, Graph Theory and its Applications, Academic Press, New York, 1970.[8] A. Jahanbani, S. Sheikholeslami and R. Khoeilar, On the spectrum of Laplacian matrix, Mathematical Problems in Engineering 2021, Article ID 8096874, 4 pp.[9] O. Jones, Spectra of Simple Graphs, 2013.https://www.whitman.edu/documents/academics/majors/mathematics/.[10] T. Raja and H. Hassim, The Laplacian spectrum of the prime order Cayley graphs of some quaternion groups, Proceedings of Science and Mathematics 8 (2022), 237-247.[11] D. Spielman, Spectral graph theory and its applications, Online Lecture Notes, 2012. http://www.cs.yale.edu/homes/spielman/eigs/.[12] X. Liu and S. Zhou, Eigenvalues of Cayley graphs, Electron. J. Combin. 29(2) (2022), 2-9.
