engleski

On the Hosoya Z index of general graphs

Motivation. The Z-counting polynomial and the Z- index, proposed by Haruo Hosoya in 1971, have been initially applied only to saturated hydrocarbons. Our aim in this report was to extend these quantities to unsaturated systems and heterosystems and to investigate the behavior of the Z-index in regard to their structural characteristics such as size, branching, cyclicity, multiple edges and heteroatoms. Method. Saturated systems were represented by simple graphs, unsaturated systems by multigraphs, heterosystems by loopgraphs and unsaturated heterosystems by loopmultigraphs. Z-counting polynomials were computed using the recurrence relation. The behavior of the Z-index was tested against the total walk count (twc) index. Results. The Hosoya Z-counting polynomial and the Z-index were computed for multigraphs, loopgraphs and loopmultigraphs. It is shown that the Z-index of these graphs parallels in most cases the results obtained for simple graphs, that is, graphs without multiple edges and loops. Conclusions. The range of applicability of the Hosoya Z-index is extended to unsaturated systems and heterosystems and it accounts well for their structural characteristics.

heterosystems; loopgraphs; loopmultigraphs; multigraphs; total walk count index; Z counting polynomial; Z-index; unsaturated(hetero)systems

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