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Title: Bounds for different spreads of line and total graphs
Author: Andrade, Enide
Lenes, Eber
Mallea-Zepeda, Exequiel
Robbiano, María
Rodríguez Z., Jonnathan
Keywords: Matrix Spread
Graph Spread
Total Graph
Line Graph
Issue Date: 15-Oct-2019
Publisher: Elsevier
Abstract: In this paper we explore some results concerning the spread of the line and the total graph of a given graph. A sufficient condition for the spread of a unicyclic graph with an odd girth to be at most the spread of its line graph is presented. Additionally, we derive an upper bound for the spread of the line graph of graphs on $n$ vertices having a vertex (edge) connectivity at most a positive integer $k$. Combining techniques of interlacing of eigenvalues, we derive lower bounds for the Laplacian and signless Laplacian spread of the total graph of a connected graph. Moreover, for a regular graph, an upper and lower bound for the spread of its total graph is given.
Peer review: yes
DOI: 10.1016/j.laa.2019.06.007
ISSN: 0024-3795
Publisher Version:
Appears in Collections:CIDMA - Artigos
OGTCG - Artigos

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