Journal
LINEAR ALGEBRA AND ITS APPLICATIONS
Volume 619, Issue -, Pages 137-145Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.laa.2021.02.018
Keywords
Signed graph; Eigenvalue; Chromatic number; Clique
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Funding
- National Natural Science Foundation of China [12001006, 11971406]
- Scientific Research Foundation of Anhui Polytech-nic University [2019YQQ024]
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This paper proves that for any nonempty signed graph Σ with n vertices, the chromatic number is greater or equal to a function involving two eigenvalues and a parameter.
For a signed graph Sigma, let chi(Sigma), lambda(1) and lambda(n) be the chromatic number, the maximum eigenvalue and the minimum eigenvalue of Sigma, respectively. This paper proves that, for any nonempty signed graph Sigma with n vertices, chi(Sigma) >= max {1 + lambda(1)/vertical bar lambda(n)vertical bar, n/n - lambda(1)}. These two bounds extend the classical spectral lower bounds of Hoffman and Cvetkovic for an ordinary graph, respectively. (C) 2021 Elsevier Inc. All rights reserved.
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