Reliability polynomials and their asymptotic limits for families of graphs

We present exact calculations of reliability polynomials R(G, p) for lattice strips G of fixed widths L(y)less than or equal to4 and arbitrarily great length L-x with various boundary conditions. We introduce the notion of a reliability per vertex, r({G},p)=lim(\V\-->infinity) R(G,p)(1/\V\) where \V\ denotes the number of vertices in G and {G} denotes the formal limit lim(\V\-->infinity) G. We calculate this exactly for various families of graphs. We also study the zeros of R(G, p) in the complex p plane and determine exactly the asymptotic accumulation set of these zeros B, across which r({G}) is nonanalytic.