Fault-diameter of generalized Cartesian products
Iztok Banič and Janez Žerovnik
In: 26th IEEE International Conference on Distributed Computing Systems Workshops (ICDCSW'06), 4-7 July 2006, Lisboa, Portugal.

Abstract

Cartesian graph bundles is a class of graphs that is a generalization of the Cartesian graph products. Let $G$ be a $k_G$-connected graph and $\DD_c(G)$ denote the diameter of $G$ after deleting any of its $c < k_G$ vertices. We prove that $\DD_{a+b+1} (G) \leq \DD_a(F) + \DD_b(B) +1$ if $G$ is a graph bundle with fibre $F$ over base $B$, $a \leq k_F$, and $b \leq k_B$. For a product of three factors $G_1$, $G_2$ and $G_3$, we show that $\DD_{a+b+c+2}(G)\leq \DD_{a}(G_1)+\DD_{b}(G_2)+\DD_{c}(G_3)+1.$

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