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    On the normalized Laplacian energy and general Randic index R_{-1} of graphs

    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. 172-190. ISSN 0024-3795

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    In this paper, we consider the energy of a simple graph with respect to its normalized Laplacian eigenvalues, which we call the L-energy. Over graphs of order n that contain no isolated vertices, we characterize the graphs with minimal L-energy of 2 and maximal L-energy of 2bn=2c. We provide upper and lower bounds for L-energy based on its general Randic index R-1(G). We highlight known results for R-1(G), most of which assume G is a tree. We extend an upper bound of R-1(G) known for trees to connected graphs. We provide bounds on the L-energy in terms of other parameters, one of which is the energy with respect to the adjacency matrix. Finally, we discuss the maximum change of L-energy and R-1(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

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