Extension of the Z Matrix to Cycle-Containing and Edge-Weighted Molecular Graphs

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 Zew matrix based on the novel Z* index is defined. In analogy to path numbers invariants kZ, k = 1, 2, ..., are introduced, and their correlation with boiling points of saturated hydrocarbons is studied.

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