Mathematical Development of the Topological Index Z. II.

Abstract

The topological index Z was proposed by the present author in 1971 for characterizing the topological structure of the carbon atom skeleton of hydrocarbon molecules, which was found to have good correlation with the boiling point of alkanes. However, recently Z was found to play a very important role in elementary mathematics and algebraic number theory by transforming algebra into geometry or graph-theory. Although a number of interesting mathematical findings were reported last year in this symposium, further new features were discovered. For example, (i) the Z index of the caterpillar graph is identical to the value of the continuant, if they are composed of the common set of elements, (ii) there are always found a series of caterpillar graphs for a given generalized Fibonacci numbers with the property, Gn=Gn•+Gn•, etc.