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Computer viruses are an extremely important aspect of computer security, and understanding their spread and extent is an important component of any defensive strategy. Epidemiological models have been proposed to deal with this issue, and we present one such here. We consider a modiÿcation of the Susceptible–Infected–Susceptible (SIS) epidemiological model… (More)

Rigorous bounds for the bond percolation critical probability are determined for three Archimedean lattices: Consequently, the bond percolation critical probability of the (3, 12 2) lattice is strictly larger than those of the other ten Archimedean lattices. Thus, the (3, 12 2) bond percolation critical probability is possibly the largest of any… (More)

The subgraph relation defines a partial order on graphs. In this paper, we determine this partial order completely for the Archimedean and Laves lattices.

We show that symmetry, represented by a graph's automorphism group, can be used to greatly reduce the computational work for the substitution method. This allows application of the substitution method over larger regions of the problem lattices, resulting in tighter bounds on the percolation threshold p c. We demonstrate the symmetry reduction technique… (More)