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The Hosoya Z matrix is originally defined only for trees. Due to a multitude of possibilities to connect pairs of vertices in a general connected undirected graph, the Z matrix could be generalized in different ways. A possibility to resolve this problem is discussed. For edge-weighted graphs, the Z ew matrix based on the novel Z * index is defined. In analogy to path numbers invariants k Z, k = 1, 2, ..., are introduced, and their correlation with boiling points of saturated hydrocarbons is studied.
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Plavšić et al. (1997) studied this question.
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