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Characterization of extremal graphs from distance signless Laplacian eigenvalues.
- Source :
-
Linear Algebra & its Applications . Jul2016, Vol. 500, p77-87. 11p. - Publication Year :
- 2016
-
Abstract
- Let G = ( V , E ) be a connected graph with vertex set V ( G ) = { v 1 , v 2 , … , v n } and edge set E ( G ) . The transmission Tr ( v i ) of vertex v i is defined to be the sum of distances from v i to all other vertices. Let Tr ( G ) be the n × n diagonal matrix with its ( i , i ) -entry equal to Tr G ( v i ) . The distance signless Laplacian is defined as D Q ( G ) = Tr ( G ) + D ( G ) , where D ( G ) is the distance matrix of G . Let ∂ 1 ( G ) ≥ ∂ 2 ( G ) ≥ ⋯ ≥ ∂ n ( G ) denote the eigenvalues of distance signless Laplacian matrix of G . In this paper, we first characterize all graphs with ∂ n ( G ) = n − 2 . Secondly, we characterize all graphs with ∂ 2 ( G ) ∈ [ n − 2 , n ] when n ≥ 11 . Furthermore, we give the lower bound on ∂ 2 ( G ) with independence number α and the extremal graph is also characterized. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00243795
- Volume :
- 500
- Database :
- Academic Search Index
- Journal :
- Linear Algebra & its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 114204284
- Full Text :
- https://doi.org/10.1016/j.laa.2016.03.017