Please use this identifier to cite or link to this item:
http://hdl.handle.net/10773/32779
Title: | On the Randić energy of caterpillar graphs |
Author: | Cardoso, Domingos M. Carvalho, Paula Dı́az, Roberto C. Rama, Paula |
Keywords: | Caterpillar graph Randi´c energy |
Issue Date: | 2022 |
Publisher: | MATCH, Faculty of Science |
Abstract: | A caterpillar graph $T(p_1, \ldots, p_r)$ of order $n= r+\sum_{i=1}^r p_i$, $r\geq 2$, is a tree such that removing all its pendent vertices gives rise to a path of order $r$. In this paper we establish a necessary and sufficient condition for a real number to be an eigenvalue of the Randi\'c matrix of $T(p_1, \ldots, p_r)$. This result is applied to determine the extremal caterpillars for the Randi\'c energy of $T(p_1,\ldots, p_r)$ for cases $r=2$ (the double star) and $r=3$. We characterize the extremal caterpillars for $r=2$. Moreover, we study the family of caterpillars $T\big(p,n-p-q-3,q\big)$ of order $n$, where $q$ is a function of $p$, and we characterize the extremal caterpillars for three cases: $q=p$, $q=n-p-b-3$ and $q=b$, for $b\in \{1,\ldots,n-6\}$ fixed. Some illustrative examples are included. |
Peer review: | yes |
URI: | http://hdl.handle.net/10773/32779 |
DOI: | 10.46793/match.87-3.729C |
ISSN: | 0340-6253 |
Publisher Version: | https://match.pmf.kg.ac.rs/electronic_versions/Match87/n3/match87n3_729-744.pdf |
Appears in Collections: | CIDMA - Artigos DMat - Artigos OGTCG - Artigos |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
On the Randic Energy of Caterpillar Graphs.pdf | 415.78 kB | Adobe PDF |
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.