Least reliable networks and the reliability domination
Abstract
A wellknown model in communication network reliability consists of an undirected graph G whose edges operate independently with the same probability p. Then the reliability R(G,p) of G is the probability that G is connected. It is known that R(G,p) is a polynomial in p and its coefficients are invariants of G. In particular, the coefficient of the leastorder term is the number of spanning trees t(G), while the coefficient of the highestorder term is the reliability domination d(G) of G. Presented is a complete characterization of graphs that achieve the minimum absolute value of d(G) over the class of nnode, eedge connected graphs. Furthermore, the class of graphs that yield minimum t(G) is shown to minimize the absolute value of d(G). These results have applications to the synthesis of leastreliable networks.
 Publication:

IEEE Transactions on Communications
 Pub Date:
 November 1990
 Bibcode:
 1990ITCom..38.2004B
 Keywords:

 Communication Networks;
 Reliability Engineering;
 Graphs (Charts);
 Polynomials;
 Trees (Mathematics);
 Communications and Radar