Cavers, Michael and Fallat, Shaun and Kirkland, Steve
(2010)
On the normalized Laplacian energy and general Randic index
R_{1} of graphs.
Linear Algebra and its Applications, 433 (1).
pp. 172190.
ISSN 00243795
Abstract
In this paper, we consider the energy of a simple graph with respect to its normalized
Laplacian eigenvalues, which we call the Lenergy. Over graphs of order n that contain
no isolated vertices, we characterize the graphs with minimal Lenergy of 2 and maximal
Lenergy of 2bn=2c. We provide upper and lower bounds for Lenergy based on its general
Randic index R1(G). We highlight known results for R1(G), most of which assume G is
a tree. We extend an upper bound of R1(G) known for trees to connected graphs. We
provide bounds on the Lenergy in terms of other parameters, one of which is the energy
with respect to the adjacency matrix. Finally, we discuss the maximum change of Lenergy
and R1(G) upon edge deletion.
Item Type: 
Article

Additional Information: 
Preprint submitted to Elsevier 
Keywords: 
normalized Laplacian matrix; graph energy; general Randic index; 
Academic Unit: 
Faculty of Science and Engineering > Research Institutes > Hamilton Institute 
Item ID: 
2188 
Depositing User: 
Professor Steve Kirkland

Date Deposited: 
13 Oct 2010 15:35 
Journal or Publication Title: 
Linear Algebra and its Applications 
Publisher: 
Elsevier 
Refereed: 
No 
URI: 

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