In this paper, we characterize the trees with the largest Laplacian and adjacency spectral radii among all trees with fixed number of vertices and fixed maximal degree, respectively.
Let G be a graph of order n andμbe an adjacency eigenvalue of G with multiplicity k≥1.A star complement H forμin G is an induced subgraph of G of order n-k with no eigenvalueμ,and the subset X=V(G-H)is called a st...Let G be a graph of order n andμbe an adjacency eigenvalue of G with multiplicity k≥1.A star complement H forμin G is an induced subgraph of G of order n-k with no eigenvalueμ,and the subset X=V(G-H)is called a star set forμin G.The star complement provides a strong link between graph structure and linear algebra.In this paper,the authors characterize the regular graphs with K2,2,s(s≥2)as a star complement for all possible eigenvalues,the maximal graphs with K2,2,s as a star complement for the eigenvalueμ=1,and propose some questions for further research.展开更多
基金Foundation item： the National Natural Science Foundation of China （No. 10601001） the Natural Science Foundation of Anhui Province （Nos. 050460102+3 种基金 070412065） Natural Science Foundation of Department of Education of Anhui Province （No. 2005kj005zd） Project of Anhui University on leading Researchers Construction Foundation of Innovation Team on Basic Mathematics of Anhui University.
文摘In this paper, we characterize the trees with the largest Laplacian and adjacency spectral radii among all trees with fixed number of vertices and fixed maximal degree, respectively.
基金supported by the National Natural Science Foundation of China(No.11971180,12271337)the Guangdong Provincial Natural Science Foundation(No.2019A1515012052)。
文摘Let G be a graph of order n andμbe an adjacency eigenvalue of G with multiplicity k≥1.A star complement H forμin G is an induced subgraph of G of order n-k with no eigenvalueμ,and the subset X=V(G-H)is called a star set forμin G.The star complement provides a strong link between graph structure and linear algebra.In this paper,the authors characterize the regular graphs with K2,2,s(s≥2)as a star complement for all possible eigenvalues,the maximal graphs with K2,2,s as a star complement for the eigenvalueμ=1,and propose some questions for further research.
