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Izvorni znanstveni članak
Mathematical Meaning and Importance of the Topological Index Z
Haruo Hosoya
| Puni tekst: engleski, pdf (772 KB) | str. 239-249 | citiraj | |
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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 10.12.2019. 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: 10.12.2019.) Vancouver Hosoya H. Mathematical Meaning and Importance of the Topological Index Z. Croatica Chemica Acta [Internet]. 2007 [pristupljeno 10.12.2019.];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: 10.12.2019.] |
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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
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