The Laplacian Spectrum of a Graph II
- 1 May 1994
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Discrete Mathematics
- Vol. 7 (2) , 221-229
- https://doi.org/10.1137/s0895480191222653
Abstract
Let G be a graph. Denote by D(G) the diagonal matrix of its vertex degrees and by A(G) its adjacency matrix. Then L(G) = D(G) - A(G) is the Laplacian matrix of G. The first section of this paper is devoted to properties of Laplacian integral graphs, those for which the Laplacian spectrum consists entirely of integers. The second section relates the degree sequence and the Laplacian spectrum through majorization. The third section introduces the notion of a d-cluster, using it to bound the multiplicity of d in the spectrum of L(G).Keywords
This publication has 14 references indexed in Scilit:
- Updating the hamiltonian problem—A surveyJournal of Graph Theory, 1991
- The Laplacian Spectrum of a GraphSIAM Journal on Matrix Analysis and Applications, 1990
- Characteristic vertices of trees*Linear and Multilinear Algebra, 1987
- Nonisomorphic graphs with the same T-polynomialInformation Processing Letters, 1986
- Permanental roots and the star degree of a graphLinear Algebra and its Applications, 1985
- Nonisomorphic trees with the same T-polynomialInformation Processing Letters, 1977
- Graph Theory with ApplicationsPublished by Springer Nature ,1976
- On a characterization of irreducibility of a non-negative matrixLinear Algebra and its Applications, 1975
- Which graphs have integral spectra?Lecture Notes in Mathematics, 1974
- Algebraic connectivity of graphsCzechoslovak Mathematical Journal, 1973