TITLE:
A Note on the Spectral Radius of Weighted Signless Laplacian Matrix
AUTHORS:
Şerife Büyükköse, Nurşah Mutlu, Gülistan Kaya Gök
KEYWORDS:
Weighted Graph, Weighted Signless Laplacian Matrix, Spectral Radius
JOURNAL NAME:
Advances in Linear Algebra & Matrix Theory,
Vol.8 No.1,
March
20,
2018
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.