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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
ISSN: 0340-6253
Publisher Version:
Appears in Collections:CIDMA - Artigos
DMat - Artigos
OGTCG - Artigos

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