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On the Spectral Properties of Graphs with Rank 4
School of Mathematics and Statistics, Qinghai Minzu University, Xining, China
- 1 School of Mathematics and Statistics, Qinghai Minzu University, Xining, China
Applied Mathematics·Volume 14 (2023)·Pages 748–763·Published 8 November 2023·DOI10.4236/am.2023.1411045
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Abstract
Let G be a graph and A ( G ) the adjacency matrix of G . The spectrum of G is the eigenvalues together with their multiplicities of A ( G ). Chang et al. (2011) characterized the structures of all graphs with rank 4. Monsalve and Rada (2021) gave the bound of spectral radius of all graphs with rank 4. Based on these results as above, we further investigate the spectral properties of graphs with rank 4. And we give the expressions of the spectral radius and energy of all graphs with rank 4. In particular, we show that some graphs with rank 4 are determined by their spectra.
KeywordsSpectral RadiusEnergyCospectral GraphsRank
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