Three new distance-based topological indices are described; two of them, D and D1 (mean distance topological indices, for any graphs, and for acyclic graphs, respectively) have a modest discriminating ability but may be useful for correlations, e. g. with octane numbers. The third index, J (average distance sum connectivity) is the least degenerate single topological index proposed till now. The properties of this promising index J are discussed in more detail.

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