On the energy of singular and non singular graphs - Andrade, Enide (2019)
Let $G$ be a simple undirected graph with $n$ vertices, $m$ edges, adjacency matrix $A$, largest eigenvalue $ρ$ and nullity $κ$. 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 $μ^{κ}$ in the expansion of characteristic polynomial, $p(μ)=\det{(μ I-A)}$ 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 $2ρ.$ Considering an increasing sequence convergent to $ρ$ a convergent increasing sequence of lower bounds for the energy of $G$ is constructed.