## Abstract

A well-known upper bound for the independence number α(G) of a graph G, due to Cvetković, is that α(G) ≤ n
^{0} + min{n
^{+}, n
^{−}}, where (n
^{+}, n
^{0}, n
^{−}) is the inertia of G. We prove that this bound is also an upper bound for the quantum independence number α
_{q}(G), where α
_{q}(G) ≥ α(G) and for some graphs α
_{q}(G) ≫ α(G). We identify numerous graphs for which α(G) = α
_{q}(G), thus increasing the number of graphs for which α
_{q} is known. We also demonstrate that there are graphs for which the above bound is not exact with any Hermitian weight matrix, for α(G) and α
_{q}(G). Finally, we show this result in the more general context of spectral bounds for the quantum k-independence number, where the k-independence number is the maximum size of a set of vertices at pairwise distance greater than k.

Original language | English |
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Pages (from-to) | 331-338 |

Number of pages | 8 |

Journal | The Electronic Journal of Linear Algebra |

Volume | 38 |

DOIs | |

Publication status | Published - 2022 |