Abstract
In recent years, the trace norm of graphs has been extensively studied under the name graph energy. In this paper, this research is extended to more general matrix norms, for example, the Schatten p-norms and the Ky Fan k-norms. Whenever possible, the results are given both for graphs and general matrices. In various contexts, a puzzling fact was observed: the Schatten p-norms are widely different for 1 ≤ p < 2 and for p ≥ 2.
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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 71, Algebraic Techniques in Graph Theory and Optimization, 2011.
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Nikiforov, V. Extremal norms of graphs and matrices. J Math Sci 182, 164–174 (2012). https://doi.org/10.1007/s10958-012-0737-z
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DOI: https://doi.org/10.1007/s10958-012-0737-z