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
References
SHOWING 1-10 OF 14 REFERENCES
The Combinatorics of Network Reliability
- Computer Science
- 1987
The reliability polynominal Edge-disjoint subgraphs Additive and multiplicative improvements Combining the bounds The k-cycle bound Computational results References Index.
Network Reliability and Algebraic Structures
- Engineering
- 1991
Overview of network reliability Approaches for calculating network reliability An algebraic formulation of network reliability problems Bounds on two-terminal reliability Enumeration of paths and…
Random graphs
- Mathematics, Computer ScienceSODA '06
- 2006
Some of the major results in random graphs and some of the more challenging open problems are reviewed, including those related to the WWW.
Network reliability and the factoring theorem
- Mathematics, Computer ScienceNetworks
- 1983
In this article, a combinatorial invariant of a graph, called the domination, is established and several important properties of the domination with regard to the topology of the graph are investigated.
Algebraic Graph Theory
- MathematicsGraduate texts in mathematics
- 2001
The Laplacian of a Graph and Cuts and Flows are compared to the Rank Polynomial.
The analysis of redundancy networks
- MathematicsTransactions of the American Institute of Electrical Engineers, Part I: Communication and Electronics
- 1958
Electrical and electronic engineers are familiar with the impedance concepts of electric networks. In such networks the parameters of interest are impedances, admittances, currents, voltages, and…
Advanced Modern Algebra
- Mathematics
- 2002
This book is designed as a text for the first year of graduate algebra, but it can also serve as a reference since it contains more advanced topics as well. This second edition has a different…
A survey of modern algebra
- Education
- 1942
This classic, written by two young instructors who became giants in their field, has shaped the understanding of modern algebra for generations of mathematicians and remains a valuable reference and…
Cambridge
- Humphrey Burton: In My Own Time
- 1969
. Let K > a> and V8: < K(K -> (/c)J). It is known that there then exists a non-trivial /c-additive 2-valued measure, v K , on the set [K] K of subsets of K of cardinality K. Definition. IF: THEOREM.…