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arXiv · 2601.01911

Some classes of connected signed graphs with girth $g$ and negative inertia index $\lceil\frac{g}{2}\rceil+1$

BeiYan Liu·Fang Duan
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Abstract

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 $i_-(Γ)=\lceil\frac{g}{2}\rceil+1$.

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BeiYan Liu, Fang Duan. 2026-01-05. Some classes of connected signed graphs with girth $g$ and negative inertia index $\lceil\frac{g}{2}\rceil+1$. https://arxiv.org/abs/2601.01911

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