The detour matrix of a (chemical) graph is defined. The detour matrix is also defined for weighted graphs. A novel method of computing the detour matrix is introduced. Some properties of the detour matrix and the distance matrix are compared. The invariants of the detour matrix (detour polynomial, detour spectrum, and detour index) are discussed, and several methods for computing these quantities are presented. The use of the detour index is analyzed and compared to the application of the Wiener number in the structure−boiling point modeling.
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Trinajstić et al. (1997) studied this question.
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