Some New Results for Reverse Graph Energies and Graph Operations

Abstract

In this paper, we establish the notions of reverse first Zagreb
energy, reverse second Zagreb energy, and reverse degree square sum energy. We show how these energies behave across various graph families.
Furthermore, we analyze the splitting graph and shadow graph energies,
i.e. their context in the complete graph family. Our research adds to the
overall knowledge about graph energies and their use within mathematical
graph theory.