不可逆k -循环图的阈值转换数

IF 1.2 Q2 MATHEMATICS, APPLIED
Ramy S. Shaheen, Suhail Mahfud, Ali Kassem
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引用次数: 1

摘要

不可逆转换过程是图上的动态过程,如果顶点满足研究开始时确定的转换规则,则对顶点进行单向状态变化(从状态0到状态1)。图G = ð V, E Þ上的不可逆k阈值转换过程是一个迭代过程,该过程首先选择一个集s0≥≥V,对于每一步t ð t = 1,2,⋯Þ,通过相邻S t−1中至少有k个邻居的所有顶点,从S t−1中得到S t。S 0称为k阈值转换过程的种子集,如果S t = V ð G Þ对于某些t≥0,则S 0是G的不可逆k阈值转换集(IkCS)。G的k阈值转换数(记为(C k ð G Þ)是G的所有ikcs的最小基数:在本文中,当r为任意时,我们确定了循环图C n ðf 1, r gÞ的C 2 ð G Þ;当r = 2,3时,我们还发现C 3 ð C n ð f1, r gÞÞ。我们还引入了C 3 ð C n ðf 1,4 gÞÞ的上界。最后,我们提出了C 3 ð C n ðf 1, r gÞÞ如果n≥2 ð r + 1 Þ和n≡0 ð mod2 ð r + 1 ÞÞ的上界。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Irreversible k -Threshold Conversion Number of Circulant Graphs
An irreversible conversion process is a dynamic process on a graph where a one-way change of state (from state 0 to state 1) is applied on the vertices if they satisfy a conversion rule that is determined at the beginning of the study. The irreversible k -threshold conversion process on a graph G = ð V , E Þ is an iterative process which begins by choosing a set S 0 ⊆ V , and for each step t ð t = 1, 2, ⋯ , Þ , S t is obtained from S t − 1 by adjoining all vertices that have at least k neighbors in S t − 1 . S 0 is called the seed set of the k -threshold conversion process, and if S t = V ð G Þ for some t ≥ 0 , then S 0 is an irreversible k -threshold conversion set (IkCS) of G . The k -threshold conversion number of G (denoted by ( C k ð G Þ ) is the minimum cardinality of all the IkCSs of G : In this paper, we determine C 2 ð G Þ for the circulant graph C n ðf 1, r gÞ when r is arbitrary; we also fi nd C 3 ð C n ðf 1, r gÞÞ when r = 2, 3 . We also introduce an upper bound for C 3 ð C n ðf 1, 4 gÞÞ . Finally, we suggest an upper bound for C 3 ð C n ðf 1, r gÞÞ if n ≥ 2 ð r + 1 Þ and n ≡ 0 ð mod2 ð r + 1 ÞÞ .
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来源期刊
Journal of Applied Mathematics
Journal of Applied Mathematics MATHEMATICS, APPLIED-
CiteScore
2.70
自引率
0.00%
发文量
58
审稿时长
3.2 months
期刊介绍: Journal of Applied Mathematics is a refereed journal devoted to the publication of original research papers and review articles in all areas of applied, computational, and industrial mathematics.
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