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Characterization of extremal graphs from Laplacian eigenvalues and the sum of powers of the Laplacian eigenvalues of graphs.
- Source :
-
Discrete Mathematics . Jul2015, Vol. 338 Issue 7, p1252-1263. 12p. - Publication Year :
- 2015
-
Abstract
- For any real number α , let s α ( G ) denote the sum of the α th power of the non-zero Laplacian eigenvalues of a graph G . In this paper, we first obtain sharp bounds on the largest and the second smallest Laplacian eigenvalues of a graph, and a new spectral characterization of a graph from its Laplacian eigenvalues. Using these results, we then establish sharp bounds for s α ( G ) in terms of the number of vertices, number of edges, maximum vertex degree and minimum vertex degree of the graph G , from which a Nordhaus–Gaddum type result for s α is also deduced. Moreover, we characterize the graphs maximizing s α for α > 1 among all the connected graphs with given matching number. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0012365X
- Volume :
- 338
- Issue :
- 7
- Database :
- Academic Search Index
- Journal :
- Discrete Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 101918467
- Full Text :
- https://doi.org/10.1016/j.disc.2015.02.006