Abstract
By applying information theory to the set of topological distances from one vertex to all other graph vertices, one obtains four new types of vertex invariants (u i,v i,x i,Y i) which are real numbers (as opposed to integers). They may be combined in many ways to afford new topological indices. One such type leads to indicesU, V, X andY which show no degeneracy for alkanes with up to 15 vertices.
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Note added in proof: 4-Trees with 18 vertices may beU, V, X andY degenerate, as will be shown: O. Ivanciuc, T.-S. Balaban and A.T. Balaban, J. Math. Chem., submitted.
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Balaban, A.T., Balaban, TS. New vertex invariants and topological indices of chemical graphs based on information on distances. J Math Chem 8, 383–397 (1991). https://doi.org/10.1007/BF01166951
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DOI: https://doi.org/10.1007/BF01166951