تقرير
All Terminal Reliability Roots of Smallest Modulus
| العنوان: | All Terminal Reliability Roots of Smallest Modulus |
|---|---|
| المؤلفون: | Brown, Jason I., DeGagné, Corey D. C. |
| سنة النشر: | 2019 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics, Mathematics - Probability, 05C31 |
| الوصف: | Given a connected graph $G$ whose vertices are perfectly reliable and whose edges each fail independently with probability $q\in[0,1],$ the \textit{(all-terminal) reliability} of $G$ is the probability that the resulting subgraph of operational edges contains a spanning tree (this probability is always a polynomial in $q$). The location of the roots of reliability polynomials has been well studied, with particular interest in finding those with the largest moduli. In this paper, we will discuss a related problem -- among all reliability polynomials of graphs on $n$ vertices, which has a root of smallest modulus? We prove that, provided $n \geq 3$, the roots of smallest moduli occur precisely for the cycle graph $C_n$, and the root is unique. Comment: 10 pages, 1 figure |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1906.02359 |
| رقم الأكسشن: | edsarx.1906.02359 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |