谱图理论中的未解决问题

doi:10.15960/j.cnki.issn.1007-6093.2023.04.003

Abstract

Abstract:

Spectral graph theory is a captivating area of graph theory that employs the eigenvalues and eigenvectors of matrices associated with graphs to study them. In this paper, we present a collection of 20 topics in spectral graph theory, covering a range of open problems and conjectures. Our focus is primarily on the adjacency matrix of graphs, and for each topic, we provide a brief historical overview.

Key words: eigenvalues, spectral radius, adjacency matrix, spectral graph theory

CLC Number:

O157.5

Lele LIU, Bo NING. Unsolved problems in spectral graph theory[J]. Operations Research Transactions, 2023, 27(4): 33-60.

Figures/Tables 2

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$ n $	$ n {\leqslant} 8 $	$ 9 {\leqslant} n {\leqslant} 11 $	$ 12 {\leqslant} n {\leqslant} 15 $	$ 16 {\leqslant} n {\leqslant} 20 $
The unique tree	$ C(1, n-2) (\cong P_n) $	$ C(2, n-4) $	$ C(3, n-6) $	$ C(4, n-8) $

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Unsolved problems in spectral graph theory

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