Negative inertia index of graphs with odd diameter
Songnian Xu, Wenhao Zhen
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Source: Crossref
Published: Sep 24, 2025
DOI: 10.1142/s1793830925501319
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Let [Formula: see text] be a simple connected graph. We use [Formula: see text], [Formula: see text] and [Formula: see text] to denote the number of negative eigenvalues, positive eigenvalues and zero eigenvalues of the adjacency matrix [Formula: see text] of [Formula: see text], respectively. In this paper, we prove that [Formula: see text] when [Formula: see text] is odd, where [Formula: see text] is the diameter of [Formula: see text]. Furthermore, when [Formula: see text] is odd, we characterize the extremal graphs for the case of [Formula: see text].
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