Tripartite Graphs with Energy Aggregation

The aggregate of the absolute values of the graph eigenvalues is called the energy of a graph. It is used to approximate the total pi-electron energy of molecules. Thus, finding a new mechanism to calculate the total energy of some graphs is a challenge; it has received a lot of research attention. We study the eigenvalues of a complete tripartite graph T-i,T-i,T-n -2i, for n >= 4, based on the adjacency, Laplacian, and signless Laplacian matrices. In terms of the degree sequence, the extreme eigenvalues of the irregular graphs energy are found to characterize the component with the maximum energy. The chemical HMO approach is particularly successful in the case of the total pi-electron energy. We showed that some chemical components are equienergetic with the tripartite graph. This discovering helps easily to derive the HMO for most of these components despite their different structures.