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Title: On the energy of singular and non singular graphs
Author: Andrade, Enide
Carmona, Juan R.
Poveda, Alex
Robbiano, María
Keywords: Energy
Singular graphs
Non 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
ISSN: 0340-6253
Appears in Collections:CIDMA - Artigos
DMat - Artigos
OGTCG - Artigos

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