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arXiv · 1410.0106

Young Graphs: 1089 et al

L. H. Kendrick
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Abstract

This paper deals with those positive integers N such that, for given integers g and k with 1< k<g, the base-g digits of N and kN appear in reverse order. Such N are called (g, k) reverse multiples. Anne Ludington Young, in 1992, developed a kind of tree reflecting properties of these numbers; N. J. A. Sloane, in 2013, modified these trees into directed graphs and introduced certain combinatoric methods to determine from these graphs the number of reverse multiples for given values of g and k with a given number of digits. We extend their work, proving Sloane's isomorphism conjectures for 1089 graphs and complete graphs, furthering his study of cyclic graphs, and proving a minor result on isomorphism.

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L. H. Kendrick. 2015-08-22. Young Graphs: 1089 et al. https://arxiv.org/abs/1410.0106

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