Abstract
Let G be a k G -edge connected graph and \(\mathcal{\overline D}_c(G)\) denote the diameter of G after deleting any of its c < k G edges. We prove that if G 1, G 2, ..., G q are k 1-edge connected, k 2-edge connected,..., k q -edge connected graphs and 0 ≤ a 1 < k 1, 0 ≤ a 2 < k 2,..., 0 ≤ a q < k q and a = a 1 + a 2 + ... + a q + (q − 1), then the edge fault-diameter of G, the Cartesian product of G 1, G 2, ..., G q , with a faulty edges is \(\mathcal{\overline D}_{a}(G)\leq \mathcal{\overline D}_{a_1}(G_1)+\mathcal{\overline D}_{a_2}(G_2)+\dots +\mathcal{\overline D}_{a_q}(G_q)+1.\)
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Banič, I., Žerovnik, J. (2007). Edge Fault-Diameter of Cartesian Product of Graphs. In: Prencipe, G., Zaks, S. (eds) Structural Information and Communication Complexity. SIROCCO 2007. Lecture Notes in Computer Science, vol 4474. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72951-8_19
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DOI: https://doi.org/10.1007/978-3-540-72951-8_19
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