In this paper, we found the bounds of the extreme eigenvalues of normalized Laplacian matrices and signless Laplacian matrices by using their traces. In addition, we found the bounds for k-th eigenvalues of normalized...In this paper, we found the bounds of the extreme eigenvalues of normalized Laplacian matrices and signless Laplacian matrices by using their traces. In addition, we found the bounds for k-th eigenvalues of normalized Laplacian matrix and signless Laplacian matrix.展开更多
This paper is concerned with the normalized Laplacian spectra of four variants of double join operations based on subdivision graph,Q-graph,R-graph and total graph.The results here generalize some well known results a...This paper is concerned with the normalized Laplacian spectra of four variants of double join operations based on subdivision graph,Q-graph,R-graph and total graph.The results here generalize some well known results about some join operations of graphs.展开更多
文摘In this paper, we found the bounds of the extreme eigenvalues of normalized Laplacian matrices and signless Laplacian matrices by using their traces. In addition, we found the bounds for k-th eigenvalues of normalized Laplacian matrix and signless Laplacian matrix.
基金Supported by the National Natural Science Foundation of China(Grant No.11961040)the Natural Science Foundation of Gansu Province(Grant No.20JR5RA418)。
文摘This paper is concerned with the normalized Laplacian spectra of four variants of double join operations based on subdivision graph,Q-graph,R-graph and total graph.The results here generalize some well known results about some join operations of graphs.
