Some signed graphs whose eigenvalues are main

Zhenan Shao and Xiying Yuan

Applied Mathematics and Computation, 2022, vol. 423, issue C

Abstract: Let G be a graph. For a subset X of V(G), the switching σ of G is the signed graph Gσ obtained from G by reversing the signs of all edges between X and V(G)∖X. Let A(Gσ) be the adjacency matrix of Gσ. An eigenvalue of A(Gσ) is called a main eigenvalue if it has an eigenvector the sum of whose entries is not equal to zero. Let Sn,k be the graph obtained from the complete graph Kn−r by attaching r pendent edges at some vertex of Kn−r. In this paper we prove that there exists a switching σ such that all eigenvalues of Gσ are main when G is a complete multipartite graph, or G is a harmonic tree, or G is a Sn,k. These results partly confirm a conjecture of Akbari et al.

Keywords: Signed graph; Adjacency matrix; Main eigenvalue; Switching (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:423:y:2022:i:c:s009630032200100x

DOI: 10.1016/j.amc.2022.127014

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