Please use this identifier to cite or link to this item:
http://hdl.handle.net/10773/27544
Title: | A lower bound for the energy of hypoenergetic and non hypoenergetic graphs |
Author: | Andrade, Enide R. Carmona, Juan Infante, Geraldine Robbiano, María |
Keywords: | Energy Hypoenergetic graph Non Hypoenergetic graph |
Issue Date: | 1-Jan-2020 |
Publisher: | University of Kragujevac, Faculty of Science |
Abstract: | Let $G$ be a simple undirected graph with $n$ vertices and $m$ edges. The energy of $G,$ $\mathcal{E}(G)$ corresponds to the sum of its singular values. This work obtains lower bounds for $\mathcal{E}(G)$ where one of them generalizes a lower bound obtained by Mc Clelland in $1971$ to the case of graphs with given nullity. An extension to the bipartite case is given and, in this case, it is shown that the lower bound $2\sqrt{m}$ is improved. The equality cases are characterized. Moreover, a simple lower bound that considers the number of edges and the diameter of $G$ is derived. A simple lower bound, which improves the lower bound $2\sqrt{n-1}$, for the energy of trees with $n$ vertices and diameter $d$ is also obtained. |
Peer review: | yes |
URI: | http://hdl.handle.net/10773/27544 |
ISSN: | 0340-6253 |
Publisher Version: | http://match.pmf.kg.ac.rs/content83n3.htm |
Appears in Collections: | CIDMA - Artigos DMat - Artigos OGTCG - Artigos |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
MATCH18619.pdf | 219.81 kB | Adobe PDF | View/Open |
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.