# Factorization of network reliability with perfect nodes II: Connectivity matrix

@article{Burgos2016FactorizationON, title={Factorization of network reliability with perfect nodes II: Connectivity matrix}, author={Juan Manuel Burgos}, journal={Discret. Appl. Math.}, year={2016}, volume={198}, pages={91-100} }

## 11 Citations

### Obtaining and Using Cumulative Bounds of Network Reliability

- Computer Science
- 2017

This chapter studies the task of obtaining and using the exact cumulative bounds of various network reliability indices, and shows how to speed up cumulative bounds obtaining by using partial sums and how to update bounds when applying different methods of reduction and decomposition.

### Quantum network reliability with perfect nodes

- Physics, Computer Science
- 2022

The concept of quantum reliability as an extension of the concept of network reliability in the context of quantum networks is introduced and a Negami like splitting formula for it is introduced.

### Sixty Years of Network Reliability

- Computer ScienceMathematics in Computer Science
- 2018

The basic concepts and results of the probabilistic model of network reliability are reviewed, as well as some recent developments in this area, and some important research directions are outlined.

### Sixty Years of Network Reliability

- Computer ScienceMath. Comput. Sci.
- 2018

The basic concepts and results of the probabilistic model of network reliability are reviewed, as well as some recent developments in this area, and some important research directions are outlined.

### Tutte polynomial general factorization

- Mathematics, Computer Science
- 2016

A new general factorization formula for the Tutte polynomial is proved, which shows a phase transition in the moduli of factorizations respect to the sharing nodes number.

### A Tutorial Exposition of Various Methods for Analyzing Capacitated Networks

- Computer Science
- 2020

This work was carried out in collaboration between both authors. Author AMAR envisioned and designed the study, performed the symbolic and numerical analysis, managed literature search and…

### Tutte polynomial general factorization for graphs on general specializations

- Mathematics
- 2016

The general unique factorization formula for the Tutte polynomial, Negami's formula, is not valid on certain specializations of the plane. The easiest example of this fact is the spanning tree…

### Maximizing k-Terminal Network Reliability in Some Sparse Graphs

- Computer ScienceIEEE/ACM Transactions on Networking
- 2021

This paper proves that the maximum reliability of terminal vertices in sparse graphs is $k, and gives equations of maximum reliability for all possible graphs in the above classes.

### Singularities in Negami's splitting formula for the Tutte polynomial

- MathematicsDiscret. Appl. Math.
- 2018

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