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Bhattacharya, A., Friedland, S. and Peled, U.N. (2008) On the First Eigenvalue of Bipartite Graphs. The Electronic Journal of Combinatorics, 15, 144.
https://doi.org/10.37236/868

has been cited by the following article:

• TITLE: On the Spectral Properties of Graphs with Rank 4

  AUTHORS: Jianxuan Luo

  KEYWORDS: Spectral Radius, Energy, Cospectral Graphs, Rank

  JOURNAL NAME: Applied Mathematics, Vol.14 No.11, November 16, 2023

  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.