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Croatica Chemica Acta, Vol. 80 No. 2, 2007.

Izvorni znanstveni članak

Mathematical Meaning and Importance of the Topological Index Z

Haruo Hosoya

Puni tekst: engleski, pdf (772 KB) str. 239-249 preuzimanja: 1.269* citiraj
APA 6th Edition
Hosoya, H. (2007). Mathematical Meaning and Importance of the Topological Index Z. Croatica Chemica Acta, 80 (2), 239-249. Preuzeto s https://hrcak.srce.hr/12863
MLA 8th Edition
Hosoya, Haruo. "Mathematical Meaning and Importance of the Topological Index Z." Croatica Chemica Acta, vol. 80, br. 2, 2007, str. 239-249. https://hrcak.srce.hr/12863. Citirano 13.06.2021.
Chicago 17th Edition
Hosoya, Haruo. "Mathematical Meaning and Importance of the Topological Index Z." Croatica Chemica Acta 80, br. 2 (2007): 239-249. https://hrcak.srce.hr/12863
Harvard
Hosoya, H. (2007). 'Mathematical Meaning and Importance of the Topological Index Z', Croatica Chemica Acta, 80(2), str. 239-249. Preuzeto s: https://hrcak.srce.hr/12863 (Datum pristupa: 13.06.2021.)
Vancouver
Hosoya H. Mathematical Meaning and Importance of the Topological Index Z. Croatica Chemica Acta [Internet]. 2007 [pristupljeno 13.06.2021.];80(2):239-249. Dostupno na: https://hrcak.srce.hr/12863
IEEE
H. Hosoya, "Mathematical Meaning and Importance of the Topological Index Z", Croatica Chemica Acta, vol.80, br. 2, str. 239-249, 2007. [Online]. Dostupno na: https://hrcak.srce.hr/12863. [Citirano: 13.06.2021.]

Sažetak
The role of the topological index, Z G, proposed by the present author in 1971, in various problems and topics in elementary mathematics is introduced, namely, (i) Pascal’s and asymmetrical Pascal’s triangle, (ii) Fibonacci, Lucas, and Pell numbers, (iii) Pell equation, (iv) Pythagorean, Heronian, and Eisenstein triangles. It is shown that all the algebras in these problems can be easily obtained, graph-theoretically interpreted, and systematically related with each other by introducing certain series of graphs whose Z G values represent the series of numbers involved therein. Finally, an ambitious conjecture is proposed: for any recursive relation of the type of Fibonacci numbers, there always exist a series of graphs whose Z-indices obey the same recursive relation. Important role of Z G in algebraic number theory is also discussed.

Ključne riječi
topological index; graph theory; elementary mathematics; recursive relation; connection between algebra and; geometry

Hrčak ID: 12863

URI
https://hrcak.srce.hr/12863

Posjeta: 1.579 *