Please use this identifier to cite or link to this item: https://research.matf.bg.ac.rs/handle/123456789/1391
Title: Walks and eigenvalues of signed graphs
Authors: Stanić, Zoran 
Affiliations: Numerical Mathematics and Optimization 
Keywords: adjacency matrix;eigenvalue;negative cycle;spectral radius;walk
Issue Date: 1-Jan-2023
Publisher: De Gruyter
Journal: Special Matrices
Abstract: 
In this article, we consider the relationships between walks in a signed graph G ˙ \dot{G} and its eigenvalues, with a particular focus on the largest absolute value of its eigenvalues ρ (G ˙) \rho \left(\dot{G}), known as the spectral radius. Among other results, we derive a sequence of lower bounds for ρ (G ˙) \rho \left(\dot{G}) expressed in terms of walks or closed walks. We also prove that ρ (G ˙) \rho \left(\dot{G}) attains the spectral radius of the underlying graph G G if and only if G ˙ \dot{G} is switching equivalent to G G or its negation. It is proved that the length k k of the shortest negative cycle in G ˙ \dot{G} and the number of such cycles are determined by the spectrum of G ˙ \dot{G} and the spectrum of G G. Finally, a relation between k k and characteristic polynomials of G ˙ \dot{G} and G G is established.
Description: 
Stanić, Zoran. "Walks and eigenvalues of signed graphs" Special Matrices, vol. 11, no. 1, 2023, pp. 20230104. https://doi.org/10.1515/spma-2023-0104
URI: https://research.matf.bg.ac.rs/handle/123456789/1391
DOI: 10.1515/spma-2023-0104
Rights: Attribution-NonCommercial-NoDerivs 3.0 United States
Appears in Collections:Research outputs

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