Fault-diameter of Cartesian product of graphs and Cartesian graph bundles
نویسندگان
چکیده
Cartesian graph bundles is a class of graphs that is a generalization of the Cartesian graph products. Let G be a kG-connected graph and Dc(G) denote the diameter of G after deleting any of its c < kG vertices. We prove that if G1, G2, . . . , Gq are k1connected, k2-connected,. . . , kq-connected graphs and 0 ≤ a1 < k1, 0 ≤ a2 < k2,. . . , 0 ≤ aq < kq and a = a1 + a2 + . . . + aq + (q − 1), then the fault diameter of G, a Cartesian product of G1, G2, . . . , Gq, with a faulty nodes is Da(G) ≤ Da1(G1) + Da2(G2)+ . . .+Daq(Gq)+1. We also show that Da+b+1(G) ≤ Da(F )+Db(B)+1 if G is a graph bundle with fibre F over base B, a ≤ kF , and b ≤ kB. As an auxiliary result we prove that connectivity of graph bundle G is at least kF + kB.
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