W. So, "Rank one perturbation and its application to the Laplacian spectrum of a graph," Linear and Multilinear Algebra, vol. 46, no. 3, pp. 193-198, 1999.W. So. Rank one perturbation and its application to the Laplacian spectrum of a graph. Linear and Multilinear Algebra, 46:193-...
Summary: Let G be a graph. The Laplacian matrix $L(G)=D(G)-A(G)$ is the difference of the diagonal matrix of vertex degrees and the 0-1 adjacency matrix. Various aspects of the spectrum of L(G) are investigated. Particular attention is given to multiplicities of integer eigenvalues an...
Summary: The paper is essentially a survey of known results about the spectrum of the Laplacian matrix of graphs with special emphasis on the second smallest Laplacian eigenvalue $λ_2$ and its relation to numerous graph invariants, including connectivity, expanding properties, isoperimetric number, ...
Merris The Laplacian spectrum of a graph II SIAM J. Discrete Math., 7 (1994), pp. 221-229 Google Scholar [14] I. Gutman The energy of a graph: old and new results A. Betten, A. Kohnert, R. Laue, A. Wassermann (Eds.), Algebraic Combinatorics and Applications, Springer-Verlag, ...
Guo Jiming, Tan Shangwang, A relation between the matching number and the Laplacian spectrum of a graph, Linear Algebra Appl., 2001,325:71–74.A relation between the matching number and Laplacian spectrum of a graph[J] . Guo Ji Ming,Tan Shang Wang.Linear Algebra and Its Applications . ...
We provide upper bounds on the perturbation of invariant subspaces of normal matrices measured using a metric on the space of vector subspaces of $\mathbb{C}^{n}$ in terms of the spectrum of both unperturbed and perturbed matrices as well as the spectrum
Let G be a simple graph of order n with Laplacian spectrum {λn, λn−1, …, λ1} where 0=λn≤λn−1≤⋅≤λ1. If there exists a graph whose Laplacian spectrum is S={0, 1, …, n−1}, then we say that S is Laplacian realizable. In 6, Fallat et al. posed a ...
Coalescence as one of the operations on a pair of graphs is significant due to its simple form of chromatic polynomial. The adjacency matrix, Laplacian matrix, and signless Laplacian matrix are common matrices usually considered for discussion under spectral graph theory. In this paper, we compute...
We prove that if $M$ is a complete hypersurface in $\\mathbb{R}^{n+1}$ which is graph of a real radial function, then the spectrum of the Laplace operator on M is the interval $[0,\\infty)$.doi:10.2140/involve.2017.10.677de Matos, Rodrigo Bezerra...
从1965年的文献开始,罗列了许多IMs of KM。依次介绍了各个方法及其优缺点,并从复杂度角度比较了两种复杂度的算法及其应用。作为一篇导论性或综述性的文章具有一定可读性。 泛读: [1] 1997 Graph Theory, Combinatorics and Application. Bojan Mohar, THE LAPLACIAN SPECTRUM OF GRAPHS.(被精读[1]所引用) ...