Signed graphs with maximal index

Published 5 Jan 2021 in math.CO | (2101.01503v2)

Abstract: The index of a signed graph is the largest eigenvalue of its adjacency matrix. For positive integers $n$ and $m\le n^2/4$, we determine the maximal index of complete signed graphs with $n$ vertices and $m$ negative edges. This settles (the corrected version of) a conjecture by Koledin and Stani\'c (2017).

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