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arXiv · 1903.09986

Continued fractions associated with the topological index of the caterpillar-bond graph

Takao Komatsu
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Abstract

In this paper, we give graphs whose topological index are exactly equal to the number $u_n$, satisfying the three term recurrence relation $$ u_n=a u_{n-1}+b u_{n-2}\quad(n\ge 2)\quad u_0=0\quad\hbox{and}\quad u_1=u\,, $$ where $a$, $b$ and $u$ are positive integers. We show an interpretation from the continued fraction expansion in a more general case, so that the topological index can be computed easily. On the contrary, for any given positive integer $N$, we can find the graphs (trees) whose topological indices are exactly equal to $N$.

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Takao Komatsu. 2019-03-24. Continued fractions associated with the topological index of the caterpillar-bond graph. https://arxiv.org/abs/1903.09986

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