The edge fault-diameter of Cartesian graph bundles.
Iztok Banič, Rija Erveš and Janez Žerovnik
Eur. j. comb. Volume 30, Number 5, pp. 1054-1061, 2009.

Abstract

A Cartesian graph bundle is a generalization of a graph covering and a Cartesian graph product. Let $G$ be a $k_G$-edge connected graph and ${\bar{\mathcal{D}}_c(G)}$ be the largest diameter of subgraphs of $G$ obtained by deleting $c < k_G$ edges. We prove that ${\bar{\mathcal{D}}_{a+b+1}(G)} \le {\bar{\mathcal{D}}_a(F)} \le {\bar{\mathcal{D}}_b(B)} + 1$ if $G$ is a graph bundle with fibre $F$ over base $B$, $a < k_F$, and $b<k_B$. As an auxiliary result we prove that the edge-connectivity of graph bundle $G$ is at least $k_F + k_B$.

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