Remarks on the Largest Eigenvalue of a Signed Graph

摘要

Let ?(1)(S) be the largest eigenvalue of a signed graph S. Wang-Yan-Qian (Linear Algebra Appl 619:137-145, 2021) and Kannan-Pragada (Linear Algebra Appl 663:62-79, 2023) extended the spectral bounds of Wilf and Nikiforov for the balanced clique number of signed graphs and derived upper bounds on ?(1)(S) in terms of its balanced clique number. In this paper, we characterize the extremal signed graphs attaining these upper bounds. Moreover, a relationship between ?(1)(S) and ?(1)(S - v) for some v ? V(S) is included.

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