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- W3193859697 abstract "Let $G$ be a graph. For a subset $X$ of $V(G)$, the switching $sigma$ of $G$ is the signed graph $G^{sigma}$ obtained from $G$ by reversing the signs of all edges between $X$ and $V(G)setminus X$. Let $A(G^{sigma})$ be the adjacency matrix of $G^{sigma}$. An eigenvalue of $A(G^{sigma})$ is called a main eigenvalue if it has an eigenvector the sum of whose entries is not equal to zero. Let $S_{n,k}$ be the graph obtained from the complete graph $K_{n-r}$ by attaching $r$ pendent edges at some vertex of $K_{n-r}$. In this paper we prove that there exists a switching $sigma$ such that all eigenvalues of $G^{sigma}$ are main when $G$ is a complete multipartite graph, or $G$ is a harmonic tree, or $G$ is $S_{n,k}$. These results partly confirm a conjecture of Akbari et al." @default.
- W3193859697 created "2021-08-30" @default.
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- W3193859697 date "2021-06-15" @default.
- W3193859697 modified "2023-09-25" @default.
- W3193859697 title "Some signed graphs whose eigenvalues are main" @default.
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- W3193859697 doi "https://doi.org/10.48550/arxiv.2106.07878" @default.
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