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 Ti,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.

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