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A Note on the Spectral Radius of Weighted Signless Laplacian Matrix
Departments of Mathematics, Faculty of Sciences, Gazi University, Ankara, Turkey
Departments of Mathematics, Faculty of Sciences, Gazi University, Ankara, Turkey
Department of Mathematics Education, Hakkari University, Hakkari, Turkey
- 1 Departments of Mathematics, Faculty of Sciences, Gazi University, Ankara, Turkey
- 2 Departments of Mathematics, Faculty of Sciences, Gazi University, Ankara, Turkey
- 3 Department of Mathematics Education, Hakkari University, Hakkari, Turkey
Advances in Linear Algebra & Matrix Theory·Volume 08 (2018)·Pages 53–63·Published 9 January 2018·DOI10.4236/alamt.2018.81006
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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.
KeywordsWeighted GraphWeighted Signless Laplacian MatrixSpectral Radius
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