Reliable Network Synthesis: Some Recent Developments

Given n nodes and m links, what is the most reliable network topology? We survey some of the recent progress that has been made on this question for the all-terminal reliability model. As well, we suggest several interesting areas for future research.

[1]  Wendy J. Myrvold,et al.  Maximizing spanning trees in almost complete graphs , 1997, Networks.

[2]  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.

[3]  Daryl D. Harms,et al.  Reliability polynomials can cross twice , 1993 .

[4]  L. R. Wang,et al.  MAXIMIZING THE NUMBER OF SPANNING-TREES OF NETWORKS BASED ON CYCLE BASIS REPRESENTATION , 1989 .

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

[6]  Jhing-Fa Wang,et al.  Reliable circulant networks with minimum transmission delay , 1985 .

[7]  A. Kelmans.  On graphs with randomly deleted edges , 1981 .

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

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

[10]  Xiao-Dong Hu,et al.  Reliabilities of chordal rings , 1992, Networks.

[11]  D. R. Shier,et al.  Maximizing the number of spanning trees in a graph with n nodes and m edges , 1974 .

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

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

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

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

[16]  F. Boesch,et al.  Super line-connectivity properties of circulant graphs , 1986 .