On Connected Graphs with Distance Eigenvalue −1 of Multiplicity at Least n−4

Yuhong Yang

doi:10.1142/s1005386723000482

On Connected Graphs with Distance Eigenvalue −1 of Multiplicity at Least n−4

Yuhong Yang

https://doi.org/10.1142/s1005386723000482

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Journal: Algebra Colloquium

Publication Date: Nov 28, 2023

Affiliation: University of Technology, Xinjiang University

#Distance Eigenvalue #Distribution Of Eigenvalue

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Abstract

Let [Formula: see text] denote the set of all connected graphs on [Formula: see text] vertices having distance eigenvalue [Formula: see text] of multiplicity [Formula: see text]. By using the distribution of the third largest distance eigenvalue and the second least distance eigenvalue of a connected graph, in this paper we completely characterize the graphs in [Formula: see text], where [Formula: see text], [Formula: see text], [Formula: see text] or [Formula: see text].

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