Some classes of connected signed graphs with girth $g$ and negative inertia index $\lceil\frac{g}{2}\rceil+1$
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908747818860544 |
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| author | Liu, BeiYan Duan, Fang |
| author_facet | Liu, BeiYan Duan, Fang |
| contents | Let $Γ$ be a signed graph. The number of negative eigenvalues of the adjacency matrix of $Γ$ is called the negative inertia index of $Γ$, which is denoted by $i_-(Γ)$. The length of the shortest cycle contained in $Γ$ is called the girth of $Γ$, and it is denoted by $g$. In this paper, we give some classes of connected signed graphs $Γ$ which satisfy the condition $i_-(Γ)=\lceil\frac{g}{2}\rceil+1$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_01911 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Some classes of connected signed graphs with girth $g$ and negative inertia index $\lceil\frac{g}{2}\rceil+1$ Liu, BeiYan Duan, Fang Combinatorics Spectral Theory Let $Γ$ be a signed graph. The number of negative eigenvalues of the adjacency matrix of $Γ$ is called the negative inertia index of $Γ$, which is denoted by $i_-(Γ)$. The length of the shortest cycle contained in $Γ$ is called the girth of $Γ$, and it is denoted by $g$. In this paper, we give some classes of connected signed graphs $Γ$ which satisfy the condition $i_-(Γ)=\lceil\frac{g}{2}\rceil+1$. |
| title | Some classes of connected signed graphs with girth $g$ and negative inertia index $\lceil\frac{g}{2}\rceil+1$ |
| topic | Combinatorics Spectral Theory |
| url | https://arxiv.org/abs/2601.01911 |