Croatica Chemica Acta, Vol. 80 No. 2, 2007.
Izvorni znanstveni članak
Mathematical Meaning and Importance of the Topological Index Z
Haruo Hosoya
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
Datum izdavanja:
12.6.2007.
Posjeta: 2.080 *