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A Note on the Spectral Radius of Weighted Signless Laplacian Matrix

DOI: 10.4236/alamt.2018.81006, PP. 53-63

Keywords: Weighted Graph, Weighted Signless Laplacian Matrix, Spectral Radius

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Abstract:

A weighted graph is a graph that has a numeric label associated with each edge, called the weight of edge. In many applications, the edge weights are usually represented by nonnegative integers or square matrices. The weighted signless Laplacian matrix of a weighted graph is defined as the sum of adjacency matrix and degree matrix of same weighted graph. In this paper, a brief overview of the notation and concepts of weighted graphs that will be used throughout this study is given. In Section 2, the weighted signless Laplacian matrix of simple connected weighted graphs is considered, some upper bounds for the spectral radius of the weighted signless Laplacian matrix are obtained and some results on weighted and unweighted graphs are found.

References

[1]  Zhang, F. (1999) Matrix Theory: Basic Results and Techniques. Springer-Verlag, New York.
https://doi.org/10.1007/978-1-4757-5797-2
[2]  Horn, R.A. and Johnson, C.R. (1985) Matrix Analysis. Cambridge University Press, New York.
https://doi.org/10.1017/CBO9780511810817
[3]  Das, K.C. (2007) Extremal Graph Characterization from the Upper Bound of the Laplacian Spectral Radius of Weighted Graphs. Linear Algebra and Its Applications, 427, 55-69.
https://doi.org/10.1016/j.laa.2007.06.018
[4]  Büyükköse, Ş. and Mutlu, N. (2015) The Upper Bound for the Largest Signless Laplacian Eigenvalue of Weighted Graphs. Gazi University Journal of Science, 28, 709-714.
[5]  Oliveira, C.S., Lima, L.S., Abreu, N.M. and Hansen, P. (2010) Bounds on the Index of the Signless Laplacian of a Graph. Discrete Applied Mathematics, 158, 355-360.
https://doi.org/10.1016/j.dam.2009.06.023
[6]  Anderson, W.N. and Morley, T.D. (1985) Eigenvalues of the Laplacian of a Graph. Linear and Multilinear Algebra, 18, 141-145.
https://doi.org/10.1080/03081088508817681
[7]  Das, K.C. (2004) A Characterization on Graphs Which Achieve the Upper Bound for the Largest Laplacian Eigenvalue of Graphs. Linear Algebra and Its Applications, 376, 173-186.
https://doi.org/10.1016/j.laa.2003.06.009

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