A Lower (Upper) Bound for the Energy of Graphs

Abstract

Let $G$ be a graph of order $n$ and size $m$. In this paper, we determine an upper bound for the energy of non-singular graph $G$ in terms of order $n$, size $m$, positive and negative indices of inertia of $A(G)$, and $det(A(G))$. We also obtain a lower bound for the energy of graph $G$, which relies on order $n$, size $m$, and maximum degree $\Delta$. Furthermore, we identify extremal graphs that attain equality in each of these bounds.