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Linearly Many Edge-Faults in 2-Bijective Connection Networks

    The class of 2-bijective connection networks (2BC networks) is defined recursively as follows: Let 2={K4} and for i 3, let i be the set of all graphs that can be constructed by taking two (possibly the same) elements R1 = (V1, E1) and R2 = (V2, E2) from i-1 (if we take the same element, we will assume they are two different copies and so V1V2 remains empty) with two bijections f1 : V1V2 and f2 : V1V2 to form the graph H = (V1V2, E1E2M1M2) where M1 = {(v, f1(v)) : vV1} and M2 = {(v, f2(v)) : vV1} such that M1M2=. This class of networks includes the class of augmented cubes. We study the structural properties of the resulting graph when “many” edges are deleted from such a network. We then mention some applications.

    Communicated by K. Qiu