Please use this identifier to cite or link to this item: http://hdl.handle.net/10773/27220
 Title: On the energy of singular and non singular graphs Author: Andrade, EnideCarmona, Juan R.Poveda, AlexRobbiano, María Keywords: EnergySingular graphsNon singular graphs Issue Date: 1-Jan-2020 Publisher: University of Kragujevac Abstract: Let $G$ be a simple undirected graph with $n$ vertices, $m$ edges, adjacency matrix $A$, largest eigenvalue $\rho$ and nullity $\kappa$. The energy of $G,$ $\mathcal{E}(G)$ is the sum of its singular values. In this work lower bounds for $\mathcal{E}(G)$ in terms of the coefficient of $\mu^{\kappa}$ in the expansion of characteristic polynomial, $p(\mu)=\det{(\mu I-A)}$ are obtained. In particular one of the bounds generalizes a lower bound obtained by K. Das, S. A. Mojallal and I. Gutman in $2013$ to the case of graphs with given nullity. The bipartite case is also studied obtaining in this case, a sufficient condition to improve the spectral lower bound $2\rho.$ Considering an increasing sequence convergent to $\rho$ a convergent increasing sequence of lower bounds for the energy of $G$ is constructed. Peer review: yes URI: http://hdl.handle.net/10773/27220 DOI: http://match.pmf.kg.ac.rs/content83n3.htm ISSN: 0340-6253 Appears in Collections: CIDMA - ArtigosDMat - ArtigosOGTCG - Artigos

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