Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 Articles in Press 2026 05 01 Spectra of Complement of Power graphs on some finite groups 15157 10.22049/cco.2026.30643.2562 EN Komal Kumari Indian Institute of Technology Kharagpur, West Bengal, India 721302 Pratima Panigrahi Indian Institute of Technology Kharagpur, West Bengal 721302 Journal Article 2025 05 22 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. https://comb-opt.azaruniv.ac.ir/article_15157_79ae7eefc7acfe2ff457633830973d05.pdf