The node cop‐win reliability of unicyclic and bicyclic graphs

DOI10.1002/net.22055zbMath1528.05046arXiv2011.10641OpenAlexW3164058326MaRDI QIDQ6065860

Ben Cameron, Unnamed Author

Publication date: 11 December 2023

Published in: Networks (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2011.10641

zbMATH Keywords

network reliabilityunicyclic graphgraph polynomialbicyclic graphcop-win graphnode reliabilityuniformly most reliablenode cop-win reliability

Mathematics Subject Classification ID

Graph polynomials (05C31) Games involving graphs (91A43) Positional games (pursuit and evasion, etc.) (91A24) Games on graphs (graph-theoretic aspects) (05C57)

Cites Work

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• The Brown-Colbourn conjecture on zeros of reliability polynomials is false
• Uniformly optimal graphs in some classes of graphs with node failures
• On bridged graphs and cop-win graphs
• Cops and robbers on intersection graphs
• On the unimodality of independence polynomials of very well-covered graphs
• Vertex-to-vertex pursuit in a graph
• Cops and robbers in a random graph
• Optimal domination polynomials
• Topological directions in cops and robbers
• On the roots of all-terminal reliability polynomials
• A Bound for the Cops and Robbers Problem
• Cops and Robbers on Graphs of Bounded Diameter
• Roots of the Reliability Polynomials
• On reliability of graphs with node failures
• On the roots of the node reliability polynomial
• Reliable circuits using less reliable relays
• On the mean subtree order of graphs under edge addition

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