Please use this identifier to cite or link to this item: http://hdl.handle.net/10773/16629
 Title: Spectra and Randic spectra of caterpillar graphs and applications to the energy Author: Andrade, EnideGomes, HelenaRobbiano, María Keywords: Spectral graph theoryEnergy of graphs Issue Date: 2017 Abstract: Let $H$ be an undirected simple graph with vertices $v_{1},\ldots ,v_{k}$ and $G_{1},\ldots ,G_{k}$ be a sequence formed with $k$ disjoint graphs $G_{i}$, $i=1,\ldots ,k$. The $H$-generalized composition (or $H$% -join) of this sequence is denoted by $H\left[ G_{1},\ldots ,G_{k}\right] .$ In this work, we characterize the caterpillar graphs as a $H$-generalized composition and we study their spectra and Randi\'{c} spectra, respectively. As an application, we obtain an improved and tight upper bound for the Energy and the Randi\'{c} energy of these interesting trees. Peer review: yes URI: http://hdl.handle.net/10773/16629 ISSN: 0340-6253 Publisher Version: http://match.pmf.kg.ac.rs/electronic_versions/Match77/n1/match77n1_61-75.pdf Appears in Collections: CIDMA - ArtigosOGTCG - Artigos

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