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Spectra of Complement of Power graphs on some finite groups | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 11 اردیبهشت 1405 اصل مقاله (434.81 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2026.30643.2562 | ||
| نویسندگان | ||
| Komal Kumari* 1؛ Pratima Panigrahi2 | ||
| 1Indian Institute of Technology Kharagpur, West Bengal, India 721302 | ||
| 2Indian Institute of Technology Kharagpur, West Bengal 721302 | ||
| چکیده | ||
| The power graph $\mathscr{P}(G)$ of a group $G$ is an undirected graph with all the elements of $G$ as vertices and where any two vertices are adjacent if and only if one is the integral power of the other. So far, no spectral results had been done for the complement of power graph on any group. In this paper, we compute the adjacency, Laplacian, and signless Laplacian eigenvalues of the complement of power graphs on finite cyclic, dihedral, and quaternion groups. Also we determine all the linearly independent eigenvectors corresponding to these eigenvalues. Moreover, we see that these eigenvectors, except possibly two, are common to all the above three type of matrices. | ||
| کلیدواژه‌ها | ||
| Eigenvalue؛ Eigenvector؛ Cyclic group؛ Dihedral group؛ Quaternion group | ||
| مراجع | ||
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[8] R.P. Panda, Laplacian spectra of power graphs of certain finite groups, Graphs Combin. 35 (2019), no. 5, 1209–1223. https://doi.org/10.1007/s00373-019-02070-x [9] M.U. Romdhini, A. Nawawi, F. Al-Sharqi, and A. Al-Quran, Spectral power graph of generalized quaternion groups, Asia Pacific Journal of Mathematics 11 (2024), 36. https://doi.org/10.28924/APJM/11-36
[10] M.U. Romdhini, A. Nawawi, F. Al-Sharqi, and A. Al-Quran, Spectral properties of power graph of dihedral groups, Eur. J. Pure Appl. Math. 17 (2024), no. 2, 591–603. https://doi.org/10.29020/nybg.ejpam.v17i2.5036
[11] D.B. West, Introduction to Graph Theory, Upper Saddle River: Prentice hall, 1996. | ||
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