Fault-diameter of Cartesian graph bundles
Iztok Banič and Janez Žerovnik
Information Processing Letters Volume 100, Number 2, pp. 47-51, 2006. ISSN 0020-0190

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 fiber $F$ over base $B$, $a \leq k_F$, and $b \leq k_B$.

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