The Laplacian eigenvalues of mixed graphs
The first part of the paper gives an upper bound for the second smallest Laplacian eigenvalue of the mixed graphs, thereby generalizing the results of \textit{M. Fiedler} [Czech. Math. J. 23, 298-305 (1973; Zbl 0265.05119)]. The second part presents two sharp upper bounds for the largest Laplacian eigenvalues of the mixed graphs in terms of the largest, smallest degrees and average 2-degrees, thereby improving and generalizing the main results of \textit{R. Merris} [Linear Algbra Appl. 285, 33-35 (1998; Zbl 0931.05053)], and \textit{J. Li} and \textit{Y. Pan} [Linear Algebra Appl. 328, 153-160 (2001; Zbl 0988.05062)].
scientific article; zbMATH DE number 1880067