浙江大学学报（理学版）2024，Vol.51Issue(2)：178-185,8.DOI:10.3785/j.issn.1008-9497.2024.02.006
最省刻度尺设计的组合差集递推算法
A recursive algorithm of combinatorial difference set design for least scale number on ruler
摘要
Abstract
For a positive integer n≥2,what is the minimum number of ticks to be engraved on an unscaled ruler of length n to measure all lengths from 1 to n.This is an unsolved problem of ruler with least number of scales.This paper clarifies the relationship between ruler with the least number of scales and the minimal graceful graph,and a combined difference recursive algorithm for calculating all the least scale values of ruler with the least number of scales is given.This algorithm calculates that the length is 3 to all the minimum scale values of the most scale-saving ruler of 40,and combined with the graph theory model,the minimum scale values of ruler with least number of scales with lengths from 41 to 82 are given.关键词
最省刻度尺/优美标号/极小优美图/优美标号算法/组合差集递推算法Key words
ruler with least number of scales/graceful labeling/minimal graceful graph/graceful labeling algorithm/combinatorial difference recursive algorithm分类
数理科学引用本文复制引用
唐保祥,任韩..最省刻度尺设计的组合差集递推算法[J].浙江大学学报（理学版）,2024,51(2):178-185,8.基金项目
国家自然科学基金资助项目(11171114). （11171114）
