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Uniformly optimally reliable graphs: A survey

https://doi.org/10.1002/net.22085

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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

inferredcites →https://doi.org/10.1002/(sici)1097-0037(199603)27:2<125::aid-net4>3.0.co;2-mopenalex-snapshot

Uniformly least reliable graphs

inferredcites →https://doi.org/10.1002/(sici)1097-0037(199709)30:2<97::aid-net4>3.0.co;2-fopenalex-snapshot

Maximizing spanning trees in almost complete graphs

inferredcites →https://doi.org/10.1002/(sici)1097-0037(199712)30:4<231::aid-net1>3.0.co;2-kopenalex-snapshot

The structure of max ?-minm?+1 graphs used in the design of reliable networks

inferredcites →https://doi.org/10.1002/(sici)1097-0037(199807)31:4<217::aid-net2>3.0.co;2-gopenalex-snapshot

Uniformly optimally reliable graphs

inferredcites →https://doi.org/10.1002/(sici)1097-0037(200003)35:2<109::aid-net2>3.0.co;2-nopenalex-snapshot

Network reliability with node failures

inferredcites →https://doi.org/10.1002/9780470745403openalex-snapshot

Rare Event Simulation using Monte Carlo Methods

inferredcites →https://doi.org/10.1002/andp.18471481202openalex-snapshot

Ueber die Auflösung der Gleichungen, auf welche man bei der Untersuchung der linearen Vertheilung galvanischer Ströme geführt wird

inferredcites →https://doi.org/10.1002/j.1538-7305.1948.tb00917.xopenalex-snapshot

A Mathematical Theory of Communication

inferredcites →https://doi.org/10.1002/jgt.3190100311openalex-snapshot

On unreliability polynomials and graph connectivity in reliable network synthesis

inferredcites →https://doi.org/10.1002/net.20300openalex-snapshot

A survey of some network reliability analysis and synthesis results

inferredcites →https://doi.org/10.1002/net.21530openalex-snapshot

Nonexistence of optimal graphs for all terminal reliability

inferredcites →https://doi.org/10.1002/net.21811openalex-snapshot

On uniformly most reliable two‐terminal graphs

inferredcites →https://doi.org/10.1002/net.21968openalex-snapshot

M ost reliable two‐terminal graphs with node failures

inferredcites →https://doi.org/10.1002/net.21977openalex-snapshot

Network reliability: Heading out on the highway

inferredcites →https://doi.org/10.1002/net.22006openalex-snapshot

The Gross–Saccoman conjecture is true

inferredcites →https://doi.org/10.1002/net.3230010307openalex-snapshot

Network reliability analysis: Part I

inferredcites →https://doi.org/10.1002/net.3230130107openalex-snapshot

Network reliability and the factoring theorem

inferredcites →https://doi.org/10.1002/net.3230150210openalex-snapshot

Combinatorial optimization problems in the analysis and design of probabilistic networks

inferredcites →https://doi.org/10.1002/net.3230200603openalex-snapshot

On the construction of optimally reliable graphs

inferredcites →https://doi.org/10.1002/net.3230210204openalex-snapshot

On the existence of uniformly optimally reliable networks

inferredcites →https://doi.org/10.1002/net.3230210404openalex-snapshot

Uniformly‐most reliable networks do not always exist

inferredcites →https://doi.org/10.1002/net.3230220206openalex-snapshot

A reliability‐improving graph transformation with applications to network reliability

inferredcites →https://doi.org/10.1002/net.3230230103openalex-snapshot

Network transformations and bounding network reliability

inferredcites →https://doi.org/10.1002/net.3230240407openalex-snapshot

On reliability of graphs with node failures

inferredcites →https://doi.org/10.1002/net.3230240504openalex-snapshot

A proof of Boesch's conjecture

inferredcites →https://doi.org/10.1002/net.3230250308openalex-snapshot

A survey of efficient reliability computation using disjoint products approach

inferredcites →https://doi.org/10.1007/978-1-4684-2001-2_9openalex-snapshot

Reducibility among Combinatorial Problems

inferredcites →https://doi.org/10.1007/978-3-319-72926-8_35openalex-snapshot

Petersen Graph is Uniformly Most-Reliable

inferredcites →https://doi.org/10.1007/bf01904874openalex-snapshot

On graphs with randomly deleted edges

inferredcites →https://doi.org/10.1007/s00373-012-1228-1openalex-snapshot

On Family of Graphs with Minimum Number of Spanning Trees

inferredcites →https://doi.org/10.1007/s11750-020-00550-5openalex-snapshot

Measuring and optimizing system reliability: a stochastic programming approach

inferredcites →https://doi.org/10.1016/0016-0032(56)90559-2openalex-snapshot

Reliable circuits using less reliable relays

inferredcites →https://doi.org/10.1016/0095-8956(74)90065-3openalex-snapshot

A certain polynomial of a graph and graphs with an extremal number of trees

inferredcites →https://doi.org/10.1016/0304-3975(79)90044-6openalex-snapshot

The Complexity of Computing the Permanent

inferredcites →https://doi.org/10.1016/j.dam.2003.06.003openalex-snapshot

On the construction of most reliable networks

inferredcites →https://doi.org/10.1016/j.dam.2019.04.022openalex-snapshot

Classes of uniformly most reliable graphs for all-terminal reliability

inferredcites →https://doi.org/10.1016/j.disc.2007.06.035openalex-snapshot

Maximally edge-connected and vertex-connected graphs and digraphs: A survey

inferredcites →https://doi.org/10.1016/j.disc.2008.08.010openalex-snapshot

Undirected simple connected graphs with minimum number of spanning trees

inferredcites →https://doi.org/10.1016/j.disc.2009.08.006openalex-snapshot

Uniformly optimal graphs in some classes of graphs with node failures

inferredcites →https://doi.org/10.1016/j.disc.2019.05.002openalex-snapshot

On the reliability roots of simplicial complexes and matroids

inferredcites →https://doi.org/10.1016/j.disopt.2021.100645openalex-snapshot

Network reliability in hamiltonian graphs

inferredcites →https://doi.org/10.1016/j.orl.2014.12.014openalex-snapshot

Topological optimization of reliable networks under dependent failures

inferredcites →https://doi.org/10.1016/j.tcs.2021.09.025openalex-snapshot

Nonexistence of uniformly most reliable two-terminal graphs

inferredcites →https://doi.org/10.1016/s0012-365x(01)00095-4openalex-snapshot

A new technique for the characterization of graphs with a maximum number of spanning trees

inferredcites →https://doi.org/10.1016/s0012-365x(97)00034-4openalex-snapshot

On the characterization of graphs with maximum number of spanning trees

inferredcites →https://doi.org/10.1016/s0095-8956(81)80028-7openalex-snapshot

Maximizing the total number of spanning trees in a graph: Two related problems in graph theory and optimum design theory

inferredcites →https://doi.org/10.1017/s0269964800001571openalex-snapshot

Some Alternate Characterizations of Reliability Domination

inferredcites →https://doi.org/10.1017/s0269964800142044openalex-snapshot

COUNTEREXAMPLES TO CONJECTURES FOR UNIFORMLY OPTIMALLY RELIABLE GRAPHS

inferredcites →https://doi.org/10.1017/s0269964800143074openalex-snapshot

SOME CONJECTURED UNIFORMLY OPTIMAL RELIABLE NETWORKS

inferredcites →https://doi.org/10.1073/pnas.17.2.125openalex-snapshot

Non-Separable and Planar Graphs

inferredcites →https://doi.org/10.1073/pnas.48.7.1142openalex-snapshot

THE MAXIMUM CONNECTIVITY OF A GRAPH

inferredcites →https://doi.org/10.1080/00207168908803727openalex-snapshot

Maximizing the number of spanning trees of networks based on cycle basis representation

inferredcites →https://doi.org/10.1109/26.61483openalex-snapshot

Least reliable networks and the reliability domination

inferredcites →https://doi.org/10.1109/drcn.2019.8713756openalex-snapshot

Building Highly Reliable Networks with GRASP/VND Heuristics

inferredcites →https://doi.org/10.1109/drcn.2019.8713759openalex-snapshot

Building Reliability-Improving Network Transformations

inferredcites →https://doi.org/10.1109/infcom.1988.12997openalex-snapshot

On the synthesis of optimally reliable networks having unreliable nodes but reliable edges

inferredcites →https://doi.org/10.1109/rndm.2017.8093016openalex-snapshot

Building uniformly most-reliable networks by iterative augmentation

inferredcites →https://doi.org/10.1109/tce.1958.6372698openalex-snapshot

The analysis of redundancy networks

inferredcites →https://doi.org/10.1109/tcs.1987.1086075openalex-snapshot

On the validity of a reduction of reliable network design to a graph extremal problem

inferredcites →https://doi.org/10.1109/tr.1986.4335422openalex-snapshot

Computational Complexity of Network Reliability Analysis: An Overview

inferredcites →https://doi.org/10.1109/tr.2018.2865707openalex-snapshot

On the Marshall–Olkin Copula Model for Network Reliability Under Dependent Failures

inferredcites →https://doi.org/10.1109/tr.2021.3061075openalex-snapshot

Universal Reliability Bounds for Sparse Networks

inferredcites →https://doi.org/10.1137/0120023openalex-snapshot

On the Invulnerability of the Regular Complete k -Partite Graphs

inferredcites →https://doi.org/10.1137/0132031openalex-snapshot

Computing the Reliability of Complex Networks

inferredcites →https://doi.org/10.1137/0208032openalex-snapshot

The Complexity of Enumeration and Reliability Problems

inferredcites →https://doi.org/10.1137/0212053openalex-snapshot

The Complexity of Counting Cuts and of Computing the Probability that a Graph is Connected

inferredcites →https://doi.org/10.1137/0214057openalex-snapshot

A Linear-Time Algorithm for Computing K -Terminal Reliability in Series-Parallel Networks

inferredcites →https://doi.org/10.1137/0220009openalex-snapshot

The Complexity of the Residual Node Connectedness Reliability Problem

inferredcites →https://doi.org/10.1142/8963#t=tocopenalex-snapshot

Spanning Tree Results For Graphs And Multigraphs: A Matrix-theoretic Approach

inferredcites →https://doi.org/10.1145/800157.805047openalex-snapshot

The complexity of theorem-proving procedures

inferredcites →https://doi.org/10.1287/opre.32.3.478openalex-snapshot

A Survey of Network Reliability and Domination Theory

inferredcites →https://doi.org/10.2307/2371086openalex-snapshot

Congruent Graphs and the Connectivity of Graphs

inferredcites →https://doi.org/10.5860/choice.37-5145openalex-snapshot

Handbook of discrete and combinatorial mathematics

inferredcites →https://doi.org/10.6028/jres.078b.023openalex-snapshot

Maximizing the number of spanning trees in a graph with n nodes and m edges

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

inferred← citeshttps://doi.org/10.1002/net.22141openalex-snapshot

More reliable graphs are not always stronger

inferred← citeshttps://doi.org/10.1002/net.22166openalex-snapshot

On the split reliability of graphs

inferred← citeshttps://doi.org/10.1002/net.70022openalex-snapshot

Infinitely Many Counterexamples to Conjectures by Boesch and Ath‐Sobel

inferred← citeshttps://doi.org/10.1007/978-3-031-16684-6_33openalex-snapshot

Bridging Reliability to Efficiency Consecutive Elegant and Simple Design

inferred← citeshttps://doi.org/10.1007/978-3-031-83438-7_23openalex-snapshot

An Algebraic Characterization of Strong Graphs

inferred← citeshttps://doi.org/10.1007/978-3-031-83438-7_24openalex-snapshot

There are Finitely Many Uniformly Most Reliable Graphs of Corank 5

inferred← citeshttps://doi.org/10.1016/j.dam.2023.06.018openalex-snapshot

On maximum graphs in Tutte polynomial posets

inferred← citeshttps://doi.org/10.1016/j.dam.2024.06.021openalex-snapshot

On the construction of locally most reliable two-terminal graphs

inferred← citeshttps://doi.org/10.1016/j.dam.2025.10.057openalex-snapshot

Most reliable graphs with reduced corank

inferred← citeshttps://doi.org/10.1016/j.disc.2025.114936openalex-snapshot

On a conjecture of regular graphs having the minimum number of induced paths of length two

inferred← citeshttps://doi.org/10.1016/j.procs.2025.10.296openalex-snapshot

Construction of infinitely many trace-minimal graphs with maximum number of spanning trees

inferred← citeshttps://doi.org/10.1016/j.tcs.2025.115327openalex-snapshot

Characterization of locally most split reliable graphs

inferred← citeshttps://doi.org/10.1029/2022wr033758openalex-snapshot

Mesoscale Modeling of Distributed Water Systems Enables Policy Search

inferred← citeshttps://doi.org/10.1111/risa.14300openalex-snapshot

Interdependent network restoration games with incomplete information and bounded rationality

inferred← citeshttps://doi.org/10.3390/math13183000openalex-snapshot

Extremely Optimal Graph Research for Network Reliability

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