Uniformly Most-Reliable Graphs and Antiholes

[1]  F. Harary THE MAXIMUM CONNECTIVITY OF A GRAPH. , 1962, Proceedings of the National Academy of Sciences of the United States of America.

[2]  A. Kelmans,et al.  A certain polynomial of a graph and graphs with an extremal number of trees , 1974 .

[3]  Eduardo Alberto Canale,et al.  A Hybrid GRASP/VND Heuristic for the Design of Highly Reliable Networks , 2019, HM.

[4]  B. Bollobás,et al.  Extremal Graph Theory , 2013 .

[5]  Xiaoming Li,et al.  On the existence of uniformly optimally reliable networks , 1991, Networks.

[6]  R. V. Slyke,et al.  On the validity of a reduction of reliable network design to a graph extremal problem , 1987 .

[7]  Ching-Shui Cheng,et al.  Maximizing the total number of spanning trees in a graph: Two related problems in graph theory and optimum design theory , 1981, J. Comb. Theory B.

[8]  Wendy Myrvold,et al.  Uniformly-most reliable networks do not always exist , 1991, Networks.

[9]  Douglas Bauer,et al.  Combinatorial optimization problems in the analysis and design of probabilistic networks , 1985, Networks.

[10]  Charles J. Colbourn,et al.  The Combinatorics of Network Reliability , 1987 .

[11]  Francis T. Boesch,et al.  On unreliability polynomials and graph connectivity in reliable network synthesis , 1986, J. Graph Theory.

[12]  Charles L. Suffel,et al.  On the characterization of graphs with maximum number of spanning trees , 1998, Discret. Math..

[13]  G. Kirchhoff Ueber die Auflösung der Gleichungen, auf welche man bei der Untersuchung der linearen Vertheilung galvanischer Ströme geführt wird , 1847 .

[14]  Guifang Wang A proof of Boesch's conjecture , 1994, Networks.

[15]  Charles L. Suffel,et al.  A survey of some network reliability analysis and synthesis results , 2009 .

[16]  N. Biggs Algebraic Graph Theory: COLOURING PROBLEMS , 1974 .

[17]  Pablo Romero,et al.  Building Reliability-Improving Network Transformations , 2019, 2019 15th International Conference on the Design of Reliable Communication Networks (DRCN).

[18]  Pablo Romero,et al.  Petersen Graph is Uniformly Most-Reliable , 2017, MOD.

[19]  Alexander Kelmans On graphs with the maximum number of spanning trees , 1996 .