Edge fault-diameter of Cartesian product of graphs

Authors:
Iztok Banič;Janez Žerovnik
Affiliations:
University of Maribor, Maribor, Slovenia and Institute of Mathematics, Physics and Mechanics, Ljubljana;University of Maribor, Maribor, Slovenia and Institute of Mathematics, Physics and Mechanics, Ljubljana
Venue:
SIROCCO'07 Proceedings of the 14th international conference on Structural information and communication complexity
Year:
2007

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Abstract

Let G be a kG-edge connected graph and Dc(G) denote the diameter of G after deleting any of its c kG edges. We prove that if G1, G2, . . . , Gq are k1-edge connected, k2-edge connected,. . . , kq-edge connected graphs and 0 ≤ a1 k1, 0 ≤ a2 k2,. . . , 0 ≤ aq kq and a = a1 + a2 + . . . + aq + (q - 1), then the edge fault-diameter of G, the Cartesian product of G1, G2, . . . , Gq, with a faulty edges is Da(G) ≤ Da1(G1) + Da2(G2) + . . . + Daq(Gq) + 1.