关于两类半群的凯莱图的消圈数
首发时间:2024-05-28
摘要:本文所谓的中值定理,是指一个取值为整数的函数能够取得介于最大值与最小值之间的任何整数值。图论中的消圈数是最小消圈集的基数,所谓消圈集,就是图中顶点的子集合,去掉其中所有顶点以及相邻接的边后图中圈完全消失。本文讨论和研究模n剩余类半群和循环半群的凯莱图是否能满足中值定理。对于第一类模n剩余类半群的凯莱图,本文研究了10以内的模n剩余类半群,只有n=6时消圈数满足中值定理。本文证明了子集合的并集的消圈数一定大于等于每个子集合的消圈数取最大. 模n剩余类半群的消圈数介于1和n之间,当子集合只取零元时,消圈数为1;子集合包含幺元时,消圈数为n。对于第二类循环半群,本文证明了循环半群的消圈数不满足中值定理,循环半群的消圈数最大为k-l,并且消圈数和消圈集以k-l为循环周期.
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on the decycling number of cayley graphs of two classes of semigroups
abstract: in this paper, the so-called intermediate value theorem in this paper means that a function with a value of integers can get any integer value between the maximum value and the minimum value. the decycling number in graph theory is the cardinality of the minimum decycling set. decycling set is a subset of vertices in a graph. all vertices and adjacent edges are removed. in this paper, we discuss and study whether cayley graphs of modulo n residual class semigroups and cyclic semigroups satisfy the intermediate value theorem. for cayley graphs of the first kind modulo n residue class semigroups, this paper studies the residual class semigroups modulo n within 10, and only n = 6 satisfies the intermediate value theorem. in this paper, we prove that the number of the union of subsets must be greater than or equal to the maximum number of the union of subsets. the number of the union of subsets is between 1 and n, and the number of the union of subsets is 1 when only consist of zero. when the subset contains the identity, the decycling number is n. for the second kind of cyclic semigroups, it is proved that the decycling number of cyclic semigroups does not satisfy the intermediate value theorem. the maximum decycling number of cyclic semigroups is k-l, and the decycling number and decycling set take k-l as the cycle period.
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