The energy of a tripartite graph

Abstract

The energy of a graph is used to approximate the total π-electron energy of molecules. Thus, finding a new technique that facilitates this task is a challenge that has received increased research attention. This paper introduces the eigenvalues of a complete tripartite graph T i,i,n-2i , for n ≥ 4, with respect to the adjacency, Laplacian, and signless Laplacian matrices. The chemical HMO approach is particularly successful in the case of the total π-electron energy. Experiments reveal that some chemical components are equienergetic with the tripartite graph. This finding helps easily derive the HMO of most of these components despite their different structures.