Year: 2018
Type: preprint
Abstract: Let $G=\left( V\left( G\right) ,E\left( G\right) \right) $ be an $\left( n,m\right) $-graph and $X$ a nonempty proper subset of $V\left( G\right) $. Let $X^{c}=V\left( G\right) \backslash X$.\ The edge density of $X$ in $G$ is given by \begin{equation*} ρ_{G}\left( X\right) =\frac{n\left\vert E_{X}\left( G\right) \right\vert }{\left\vert X\right\vert \left\vert X^{c}\right\vert }, \end{equation*} where $E_{X}\left( G\right) \ $ is the set of edges in $G$ with one end in $% X $ and the other in $X^{c}$. The Laplacian spread of a graph is the difference between the greatest Laplacian eigenvalue and the algebraic connectivity. In this paper, we use the edge density of some nonempty proper subsets of vertices in $G$ to establish new lower bounds for the Laplacian spread. Also, using some known numerical inequalities some lower bounds for the Laplacian spread of a graph with a prescribed degree sequence are presented.
Source: arXiv (Cornell University)
Institutions: University of Aveiro, Universidad Católica del Norte
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funders: Conselho Nacional de Desenvolvimento Científico e Tecnológico, Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro, Center for Research and Development in Mathematics and Applications, Fundação para a Ciência e a Tecnologia, Comisión Nacional de Investigación Científica y Tecnológica
OpenAlex ID: W2806456073