Some Bounds on the Energy of Graphs with Self-Loops regarding ${\lambda }_1$ and ${\lambda }_n$

Minghua Li, Yue Liu

Let $G_S$ be a graph with $n$ vertices obtained from a simple graph $G$ by attaching one self-loop at each vertex in $S\subseteq V(G)$. The energy of $G_S$ is defined by Gutma…