DocumentCode :
588904
Title :
New Bounds of the Nordhaus-Gaddum Type of the Laplacian Matrix of Graphs
Author :
Tianfei Wang ; Bin Li ; Jin Zou ; Feng Sun ; Zhihe Zhang
Author_Institution :
Sch. of Math. & Inf. Sci., Leshan Normal Univ., Leshan, China
fYear :
2012
fDate :
17-18 Nov. 2012
Firstpage :
411
Lastpage :
414
Abstract :
The Laplacian matrix is the difference of the diagonal matrix of vertex degrees and the adjacency matrix of a graph G. In this paper, we first give two sharp upper bounds for the radius of the Laplacian spectrum of G in terms of the edge number, the vertex number, the largest degree, the second largest degree and the smallest degree of G by applying non-negative matrix theory and graph theory. Then, two upper bounds of the NordhausGaddum type are obtained for the sum of Laplacian spectral radius of a connected graph and its connected complement. Moreover, we determine all extremal graphs which achieve these upper bounds. Finally, one numerical example illustrate that our results are better than the existing results in some sense.
Keywords :
graph theory; matrix algebra; number theory; Laplacian matrix; Laplacian spectrum radius; Nordhaus-Gaddum type; adjacency matrix; connected graph; diagonal matrix; graph theory; nonnegative matrix theory; sharp upper bounds; vertex degrees; vertex number; Educational institutions; Eigenvalues and eigenfunctions; Electronic mail; Laplace equations; Linear algebra; Symmetric matrices; Upper bound; Laplacian matrix; Laplacian spectral radius; Nordhaus¨CGaddum; complement;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Computational Intelligence and Security (CIS), 2012 Eighth International Conference on
Conference_Location :
Guangzhou
Print_ISBN :
978-1-4673-4725-9
Type :
conf
DOI :
10.1109/CIS.2012.98
Filename :
6405956
Link To Document :
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