We discuss the eigenvalues of real symmetric matrices, especially focus on the eigenvalues of matrix BBT where B expresses the adjacency relation between two parts of a semiregular bipartite graph. Based on this, the existence of two kinds of (r, k)-semiregular bipartite graphs are excluded.

Real symmetric matrices;Eigenvalues;Semiregular bipartite graph

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This work is supported by the Provincial Natural Science Foundation of Xinjiang: “Study on the spectral characterization of graphs with few distinct eigenvalues” (fund project number 2022D01A252).

DOI： https://doi.org/10.62639/sspjinss11.20240104

Published： 2024