Petersen Graph is Uniformly Most-Reliable

  • Guillermo RelaEmail author
  • Franco Robledo
  • Pablo Romero
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10710)


A celebrated problem in network optimization is the all-terminal reliability maximization. We want to communicate a fixed number n of terminals, but we have a fixed budget constraint m. The goal is to build m links such that the all-terminal reliability is maximized in the resulting graph. In such case, the result is a uniformly most-reliable graph. The discovery of these graphs is a challenging problem that launched an interplay between extremal graph theory and computational optimization.

In this paper, we mathematically prove that Petersen graph is uniformly most-reliable. The paper is closed with a conjecture on the existence of other uniformly most-reliable graphs.


Network reliability analysis Uniformly most-reliable graphs Petersen graph 



This work is partially supported by Project 395 CSIC I+D Sistemas Binarios Estocásticos Dinámicos. We wish to thank Dr. Louis Petingi for his valuable comments on t-optimality throughout the writing of this manuscript.


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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Facultad de Ingeniería, Instituto de Matemática y Estadística, IMERLUniversidad de la RepúblicaMontevideoUruguay

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