New lower bounds for the Randić spread

• Main Author: Andrade, Enide
• Publication Date: 2018
• Other Authors: Freitas, Maria Aguieiras A. de, Robbiano, María, Rodríguez, Jonnathan
• Format: Article
• Language: eng
• Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
• Download full: http://hdl.handle.net/10773/22409
• topic: Matrix spread; Randić spread; Randić matrix; Normalized Laplacian spread; Laplacian spread; Regular graphs; Nullity; Independence number

Let $G=\left( \mathcal{V}\left( G\right) ,\mathcal{E}\left( G\right) \right) $ be an $\left( n,m\right) $-graph. The Randi\'{c} spread of $G$, $s_{R}(G)$, is defined as the maximum distance of its Randi\'{c} eigenvalues, disregarding the Randi\'{c} spectral radius of $G$. In this work, we use numerical inequalities and bounds for the matricial spread to obtain relations between this spectral parameter and some structural and algebraic parameters of the underlying graph such as, the sequence of vertex degrees, the nullity, Randi\'{c} index, generalized Randi\'{c} indices and its independence number. In the last section a comparison is presented for regular graphs.