Spectra of Complement of Power graphs on some finite groups

Articles in Press

Document Type : Original paper

Authors

1 Indian Institute of Technology Kharagpur, West Bengal, India 721302

2 Indian Institute of Technology Kharagpur, West Bengal 721302

Abstract

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.

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References

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Communications in Combinatorics and Optimization

Articles in Press, Accepted Manuscript
Available Online from 01 May 2026

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